In addition to the Claw skill, to use two claws you must have the Two Weapons skill that has Florentine as a prerequisite, or the Style Master skill. Florentine and Claw on its own would allow you to weild a claw and a short weapon, but not two claws.
As another note: If you have Claws and Florentine, are able to wield a Claw and a Small Weapon, though you will also need to have an appropriate skill to actually use the Small Weapon in question (Small Weapon, One-Handed Edge, One-Handed Blunt). Without that non-Claw weapon skill, Claws + Florentine is effectively useless.
The same principle applies with Claws + Florentine + Two Weapons. You'll be able to use two Claws, but you'll need One-handed Edge/Blunt if you want to use a Claw and a Short/Long Weapon at the same time.
So all I need is two weapon skill? I don't need florentine? I plan to either use just claws at time or use my kukri. I only plan to duel wield when I use claws.