It will take some work, but it's perfectly doable.

Enemies with special defenses

The players won't have access to see invisible, flight, magic weapons, or ghost touch. Therefore, if you include enemies that can fly, or have DR/magic, or are intangible, these will be huge challenges, and may be downright impossible. The easy solution is simply to not include such enemies, but the more interesting way is to treat them as nigh-invulnerable enemies that the heroes will have to figure out how to defeat. In a normal Pathfinder game, a ghost is a normal critter with a +2 CR template pasted on top, and requires some minimal preparation to defeat. In a low-magic Pathfinder game, a ghost is a mystery: why did they become a ghost? How can you persuade them to pass on, or at least let the party pass by peacefully? Can you persuade the local priest to perform an exorcism, and will it even work? Instead of "find monster, insert fireball," these types of encounters are now role-playing challenges, because they can't be solved any other way!

Alternatively, you can simply strip out the special defenses from enemies. Pathfinder assumes you have level-appropriate counters to special abilities anyway, so by removing those special defenses, you aren't going too far from the original intent. Adjusting the CR is left as an exercise for the GM, because it's going to take a fair amount of trial-and-error to determine what the right balance is.

Fixing armor class, and other numbers issues

Pathfinder assumes that both attack bonuses and defenses will be augmented by magic items. This partially balances out if the players don't have magic items, but consider giving everyone a +1 bonus to AC and all defenses every four levels. Don't make them pay a feat for it, just give it to them.

While you're at it, give your players bonus XP for the monsters they defeat, by calculating the XP as if the monsters were a higher CR. Since they're operating without magic, every encounter is going to be harder than what the DMG "expects" when it calculates XP per CR.

What will they do with their money?

Your players won't be able to buy gear that personally enhances their ability to make things dead faster, or grant them new solutions. If you keep to the normal loot rules, then the party will have far, far more money than they know what to do with. You have two options here: give them less money, or give them something to do with that money.

Let them invest in mercenary companies or land holdings. Let them become influential in the church, or their hometown, or even their country as their economic might and donations in the right places give them power that they would never be able to take with a sword. Favors in high places give characters some very powerful options.

Recovery after combat

This will require explicit house rules; you'll need to accelerate natural healing (heal a percentage of HP per day instead of a flat amount?), allow Heal checks to do much more than they normally do, grant the local clergy some extremely localized healing powers (they can heal people brought to their church, but not outside of their place of worship), and/or make this a political game rather than a hack-and-slash game.

If everyone's having fun, then it's a good game. It doesn't matter if the characters aren't optimized: as long as they feel like they're making a difference in the world and they're enjoying the game, then you're doing it right. The characters will be balanced, more or less: they all don't have access to magic, so intra-party balance isn't as much of a problem. You'll see that the players lack all of the magic-based solutions that you'd expect in a normal Pathfinder game, and you'll select the enemies more carefully, but things will work out fine. Let your players know that things will be a bit different than normal, and your players will go along with it; they requested this kind of game, after all.

Fighter, Monk, Wizard, Sorcerer, Cleric, Shugenja (from Complete Divine), Rogue and Ninja (from Complete Adventurer)

Unfortunately, you have selected a massively disparate subset of the classes. Fighter, monk, ninja, and rogue are four of the weakest classes published for all of 3.5 (with Complete Adventurer’s ninja actually probably the worst here), while cleric, shugenja, sorcerer, and wizard are four of the strongest classes published (especially the cleric and wizard).

And ultimately, those spellcasters are so powerful that no one without spellcasting is going to be able to keep up if they’re played at anything like their potential.

If you are going to be selecting a very-limited subset of the classes, I suggest that you take the opportunity to choose better designed classes which have tighter overall balance. Your warriors are not powerful enough, your spellcasters are too powerful.

You can ignore the advice for everyone but the fighter and the monk – I still do strongly recommend the swordsage and warblade there – but even those improved options won’t be able to keep up with those spellcasters, at least not unless the people playing them are underplaying their power quite a lot. Therefore, I’d like to offer a more “complete” recommendation for every class on your list.

In all cases, I have carefully chosen the replacement class so that it can be a “drop-in” replacement – you don’t have to make up a new place in your setting for warblades, just use the warblade’s stats and rules and call it “fighter.”

Stronger warriors

The more “direct” answer to the question, there definitely are superior options for playing a “fighter” or “monk” than the fighter class or monk class. Note, however, that even these are still a far cry from the spellcasters you have selected (and, indeed, still are not quite up to the ability of even the weaker spellcasters I recommend below).

Instead of fighter, consider the warblade

The warblade from Tome of Battle: The Book of Nine Swords is an intelligent master-of-arms, a savvy tactician and a well-honed veteran of battle. His ability to master weapons is without parallel, and in battle he is relentless and iconic, rallying his allies around him.

Instead of monk or ninja, consider the swordsage

Also from Tome of Battle, the swordsage could be monk or ninja, depending on the particular choices that you make. A “monk-like” swordsage would probably focus more on Diamond Mind and Setting Sun maneuvers, while a “ninja-like” swordsage would likely focus on Shadow Hand and Tiger Claw – but either would be remiss to ignore those other disciplines.

Instead of rogue, consider the factotum

Dungeonscape’s factotum is basically “the class Indiana Jones would take if he were in D&D.” Factota do a little bit of everything, and do it well. They use their wits and cunning to make it up as they go along, and are the best skill-monkeys in the game, bar none. Awesome, super-fun class.

Weaker Spellcasters

I wrote an answer dedicated to this question here, but because that question was overly-broad, my answer was overly-long.

But the idea is still sound: the over-powered spellcasters you have chosen could be replaced quite well by other spellcasters that fulfill similar roles and have similar narrative backgrounds. Note that these spellcasters are still very powerful, however; using these is insufficient to make the fighter, monk, or ninja classes play on even footing. Even the superior classes I recommend above are at something of a disadvantage compared to most of these; the gap is just much narrower.

For this game, I strongly recomment the following replacements:

Instead of cleric, consider the divine bard

Bards are viable warriors, while not being excellent at it. The cleric would make a far better warrior than any of your warrior classes. The bard has some solid healing spells, especially when divine, and their music makes them fantastic leaders-of-men.

Alternatively, the incarnate might be excellent

The incarnate from Magic of Incarnum is an excellent replacement, flavor-wise, for a cleric, with a strong religious theme (an evil-aligned incarnate is supposed to literally be evil incarnate). Their powers lends themselves a bit more to the skill-monkey/support role than the warrior/healer role, but they’re overall an excellent class and judiciously awarding wands of cleric spells can make up a huge part of the difference.

If you specifically wanted the warrior-priest, crusader is for you

I generally recommend replacing cleric with classes that are less devastating at armed combat, because I tend to feel that the cleric’s prowess there makes it difficult to justify the existence of, e.g., paladins. But since you have not selected paladins in the first place, you might be looking for a more martial bent from your divine class. If so, the crusader from Tome of Battle: Book of Nine Swords is perfect – he heals his allies as he smites his enemies, and as a rallying point and commander of battle, he knows few peers.

Also, crusader is one of my favorite classes in the game, and my #1 recommendation to new players.

Instead of shugenja, consider the ... actually, shugenja’s probably OK

Shugenja is the weakest of the spellcasting classes that you have listed, and while it is more powerful than the other classes I have mentioned here, it’s probably close enough so as not to cause problems.

Instead of sorcerer, consider the dragonfire adept

Sorcerers, in 3.5, are thought to base their magic powers on trace draconic ancestry. The dragonfire adept from Dragon Magic, on the other hand, obviously gets their power from dragons. They gain a breath weapon and a number of invocations, which are at-will spell-like abilities. Similar style to a sorcerer, at a lower power level. Like the warlock, which I recommend as a replacement for wizard, below, dragonfire adepts tend to be a little on the low side, in terms of invocations known. Allowing them to learn a new invocation every level except those in which they gain a new breath effect is a simple solution that I have found works well.

Instead of wizard...

Instead of enchanter or illusionist, consider the beguiler

Beguilers, from Player’s Handbook II, get a small, specific spell list, tailored towards the casting of enchantments and illusions. They do get some opportunities to add to their list, but few enough to keep them under control. They’re also a lot of fun.

The beguiler might be the most powerful class here (I don't have enough experience with shugenjas to say for sure), so you may want to reduce it somewhat. Their armored spellcasting is a minor boon they can easily afford to lose, and as an Int-based class, 6+Int skill points is quite a bit – 4+Int might be more appropriate. Removing some or all of glitterdust, haste, solid fog, and/or time stop from their spell list might be good choices.

Instead of necromancer, consider the dread necromancer

Heroes of Horror’s dread necromancer is actually better than the wizard-necromancer at raising undead minions, but the dread necromancer spell list is tightly limited, like the beguiler’s, to enforce the focus on necromancy. Again, smaller list with carefully-controlled opportunities to expand it do a lot to limit the power of the wizard.

As will become a theme, changing the dread necromancer’s spellcasting to Intelligence rather than Charisma will make them more “wizardly.” The split between Intelligence for spells and Charisma for Rebuke Undead is also probably a good thing, and will slightly (but noticeably) play up the more “wizardly” necromancy of curses and debuffs, rather than the minion-master undead-army-raising that you get with Rebuke Undead, which I consider a good thing.

I’d also consider losing the ability to cast in light armor. It’s not especially powerful (it is easy to avoid Arcane Spell Failure), but the dread necromancer is on the higher-end of classes presented here, so chipping away at that is desirable. Plus, I recommended removing it from the beguiler (enchanter) and warlock (generalist wizard), leaving the dragonfire adept (sorcerer) and warmage (evoker) the only ones who have it: that seems appropriate.

Instead of evoker, consider the warmage

The warmage from Complete Arcane is the evocation equivalent of the beguiler or dread necromancer. Unfortunately, being blasting-only does leave the warmage a little flat, but they are still capable enough for keeping up with my other suggestions.

Since you want the warmage to be replacing an evoker-wizard, I would switch the spellcasting to Intelligence. This has the added bonus of making the Warmage Edge feature more useful (usually, outside of very-low levels, the bonus it provides is too small to justify investing much in Intelligence, and it just ends up being a trap, tricking players into putting too much into Intelligence).

Instead of wizard, consider the warlock

Another entry from Complete Arcane, the warlock is similar to the dragonfire adept, but much more strongly arcane, with abilities to conjure, dispel, divine, and transmute, not to mention their iconic eldritch blast. These make decent generalists; a bit on the weak side, so consider increasing their number of invocations known. I find having 1/level goes a long way. Also, eldritch blast goes up 1d6 every odd level... until 13th level, where it goes up every three levels. No one knows why it slows down like that, but it’s pretty common to just ignore that and use 1d6 per odd level, and that works well.

Making the warlock intelligence-based would also be a nice improvement of his wizardly-ness. It also helps the skill situation, though even with an Intelligence focus I’d still give the poor guy 4+Int skills. Losing the ability to invoke in light armor may be appropriate, especially if this justifies some more invocations known (say, 1/level, plus an additional 1 each time you reach a new tier of invocation? That would be awesome).