If you want to give your fighter more access to magic without rebuilding you're going to be limited to skills, feats, and magical items. None of these will give your fighter heavy magical abilities, instead letting you play the character as someone who has learned basic magic.
Skills
The skills that increase magical knowledge are:
Knowledge (Arcana) - represents general knowledge your fighter has acquired about magic; what an arcane symbol means, how the local mage guild heirarchy is organized. Stuff he would learn in school or from talking to spellcasters.
Spellcraft - much more specialized knowledge about specific magical effets. While Knowledge (Arcana) is theoretical studies, this is applied studies. Being able to recognize magical effects, figure out what spells are being cast. Knowledge gained by seeing magic in action, how it's been used.
Use Magic Device - knowing how to use the magical items that are common to spellcasters; staff, wands, scrolls, etc. The Evil Necromancer has defeated the parties fighter and is now monologuing to the rest of the party about their imminent defeat. The tired fighter rolls over, grabs the wand of fireballs from the necromancers belt and make a brilliant quip as fire blossoms around them.
Feats
There aren't a lot of feats that contribute to magical abilities. The first one I recommend is Able Learner from Races of Destiny. This feat treats all skills as being in-class skills. This will allow you to level up the above skills quicker.
The other feat that is useful is Magical Training, from the Players Guide to Faerun. It allows your character to cast three 0-level arcane spells per day as either a wizard or sorcerer.
Items
Have your character carry around magical items that are commonly associated with spellcasters. Staves, scrolls, wands. Combined with Use Magic Device this allows the fighter to have access to magical abilities.
A staff is an excellent choice of a magical item for this type of fighter. They can use it as their melee weapon, and use the magical abilities within it. A great surprise tactic when fighting: thrust, thrust, parry, Cone of Cold.
Sure, mechanical/non-magical equivalents would be a fluffy way to satisfy as aspect of his role-playing. But how about you try something interesting?
Word of your superstition and abstinence against magical gear has
spread and intrigued a number of people. You've awakened old fears of
harmful magical auras, and new prides in personal strength. Scholars
and philosophers start sending you mail asking you questions or for
instructions in how to live as a 'magi-Luddite' as the trend is being
called. You become a minor celebrity with people asking to follow in
your footsteps.
In short, give him the leadership feat. With the string that if he started using magical gear (in public) his following would abandon him.
Best Answer
This is a matter of plot, not rules, but warforged have the stats you want
In Eberron, warforged are made in Creation Forges of either Cannith or (spoilers) Quori design. The renegade mastermaker prestige class from Magic of Eberron details one way that a flesh-and-blood creature can become a living construct, there through literally grafting warforged components onto his or her body. This implies that it can be done.
And certainly, binding souls into constructs has a long and storied history in the sorts of narratives that D&D is based on. Nothing in Eberron, to my knowledge, actually describes such a thing taking place explicitly, and thus there are no rules for actually doing it, but it’s trivial to imagine fitting within Eberron.
So just play a warforged, but say you came about in a way that is different from other warforged. For that matter, how Creation Forges actually work is intentionally left a mystery for the DM to do with as he likes. It’s entirely possible that they are pulling souls from somewhere (most likely Dolurrh, but not necessarily). Such a character could easily have come from a Creation Forge accident. Eberron also has Eldritch Machines, literally monolithic blocks of Plot, which could certainly do this. And that’s assuming this isn’t just a grandiose variation on trap the soul or magic jar or even reincarnate.
I would not bother with rules for this, I would just write it into the backstory and use the warforged rules. If the actual event is to take place during the game, I would just describe the scene, and have you erase your prior racial stats and replace them with warforged.