Enchanting natural weapons
You can't place magical weapon properties directly onto natural weapons. That would be like a monk getting his fist made into a +1 Flaming Fist. In the case of the monk, you buy fist wraps. In the case of the fighter, you buy a sword. In the case of the monster with natural weapons, you buy yourself a copy of Savage Species and flip to page 58: Necklace of Natural Weapons.
It takes up the magic item neck slot, but you can actually have the enhancement bonuses applied to multiple natural weapons for a base cost of 600 gp plus the enhancement bonus. You can then multiply the cost by the number of natural weapons affected, so in the case of the nimblewright, 2 rapier-hands at +1 each would be 5,200 gp.
Yes the book says to multiply the entire cost, including the cost of the necklace itself. For semantics I would say that the necklace holds a number of matching engraved beads equal to the number of natural weapons affected. So two claws, a bite, and a tail would be four beads.