Replacing a claw attack with an unarmed strike
Sorry, but no. Unarmed strikes use a weird hybrid of the rules for manufactured and natural weapons, but for the purposes of full-attacks, they work like manufactured weapons. That is, you get iteratives with them, but if you can only combine them with natural weapons by making those natural weapons secondary (−5 attack penalty, only ½Str to damage).
The first rule that you quote is specifically about spells and effects. A full-attack is not either of those.
Claws and lack of offhand unarmed strikes
Feral Combat Training does mean that anything from the monk’s unarmed-strike-improving class features can apply to natural weapons, and that can include the bit about never being offhand.
However, claws and other natural weapons are never “offhand” to begin with. The term “offhand” only applies when using two-weapon fighting, and that combat option does not interact with natural weapons (aside from the attack penalty, which applies to all attacks). So the fact that the monk class feature, combined with Feral Combat Training, says that natural weapons are never offhand does not do anything because that was already true.
Instead of “main hand” and “offhand,” natural weapons are either “primary” or “secondary.” These are different. When combined with manufactured weapons (or unarmed strikes) in a given full-attack, all natural weapons are secondary: they receive the −5 penalty and get only ½Str to damage. Neither the monk class nor Feral Combat Training does anything about treating them as secondary or removing or reducing the penalties for being secondary.
So whether you have Feral Combat Training or not, your full-attack using unarmed strikes is:
Unarmed Strike, Claw (−5), Claw (−5), Claw (−5)
If you have Feral Combat Training, the claws do benefit from the improved base damage dice of unarmed strike, however, even if they’re still stuck with ½Str to damage.
Two-Weapon Fighting, Feral Combat Training
If you are actually using two-weapon fighting, the provision about monks never having offhand unarmed strikes meaningfully applies only to the unarmed strike. It “applies” to the claws, but does nothing for them.
So, for example, if your two weapons are a sai and an unarmed strike, and you have the Two-Weapon Fighting feat, your attack routine would be:
Sai (−2), unarmed strike (−2), claw (−5), claw (−5)
The unarmed strike would add your full Strength to its damage, however. Note that I assumed that the sai took up one of your claw-hands. I did not wish to get into the debate about whether one can use two unarmed strikes as part of two-weapon fighting.
You didn’t ask, but about Flurry of Blows
All of the statements above about full-attack apply equally well to flurry of blows, except that you need Feral Combat Training to use natural weapons in a flurry at all, and flurry of blows cannot be combined with two-weapon fighting because of Paizo nonsense.
Personal recommendation
For the record, monks, natural attacks, and how they combine, these are some of the worst things in Pathfinder. The rules are confusing, complicated, and the result works very poorly. I suggest you save yourself a headache and just... not.
No, it doesn't work.
But with the Weapon Versatility feat (requires Weapon Focus) from the Undead Slayer's Handbook, you can use the Estoc with Slashing Grace just fine.
Benefit: When wielding a weapon with which you have Weapon Focus, you can shift your grip as a swift action so that your weapon deals bludgeoning, piercing, or slashing damage instead of the damage type normally dealt by that weapon. You may switch back to the weapon’s normal damage type or another damage type as a swift action. If your base attack bonus is +5 or higher, using this feat is a free action instead.
However, there are other options that you can look into:
Mythic Weapon Finesse - only available if you have mythic. Allows the character to add dex to damage to all finessable weapons.
4th level of a swashbuckler archetype called Whirling Dervish. This applies to all weapons that work with Swashbuckler finesse plus scimitars.
At 1st level, a swashbuckler gains the benefits of the Weapon Finesse feat with light or one-handed piercing melee weapons, and she can use her Charisma score in place of Intelligence as a prerequisite for combat feats. This ability counts as having the Weapon Finesse feat for purposes of meeting feat prerequisites.
- 3rd level of Unchained Rogue (and again at 11th and 19th levels) allows one to select a single finessable type of weapon so you can use dex to damage with that type of weapon.
Finally, if the Path of War from Dreamscarred Press (third party publisher) is allowed, you have Deadly Agility, which allows you to use dex to damage on any light or finessable weapon.
Best Answer
You are correct, the fact that the benefit section is talking about bucklers has no bearing on the special section, since the special section only requires you to have the feat, not actually be using it. If it said “While using this feat, a monk [...],” you would have a much harder time making that argument, but it doesn’t say that.
The name and fluff of the feat also reference a “shield,” rather than “buckler” specifically, so there is some reason to think this may even have been intentional.
That said, taking this feat and then not using a buckler seems like a poor choice—a heavy shield has only +1 shield bonus more to AC than a buckler, and has several other drawbacks that this shield lacks. Since shield bonuses to AC don’t count towards touch attacks, +1 is very close to worthless. Armored AC is (by far) the weakest defense in the game, and after the basics (best armor you can use without losing class features or needing to spend a feat), it’s basically never worth investing in on its own.
Which is another reason to expect it’s fine to allow it to be used with non-bucklers: the feat is quite a lot weaker that way anyway. Please don’t fall into that trap though.