If I use Claw Blades, which turn my natural claw attacks into light slashing weapons (weren't claws already Light slahsing weapons!?),
Claws are not light slashing weapons, they are light slashing/bludgeoning natural weapons. The difference is subtle but there are rules that cover them separatedly, specially for natural weapons.
The difference being that manufactured weapons can be enchanted (ie: made into magical items), while natural weapons cannot, they can gain bonuses from spells and certain magic items, but by themselves, they cannot be enhanced magically. Natural weapons can also be enhanced by feats that enhance natural attacks, while manufactured weapons cannot.
does that mean I can't perform "2 Claws" attack routine anymore
Yes, that is exactly the drawback from using Claw Blades, you gain the ability to keep your damage die, gain an +1 enhancement on the damage, and it becomes a manufactured weapon for all purposes, including enchanting and enhancing them. And they can also be used on interative attacks from high BAB.
Similar to Brass Knuckles for monks.
However, the Rending Claw Blades seems to point that Claw Blades should work just like your claws, despite being manufactured weapons now.