nogz
Member
I'm pretty sure the claws only work in their respective caves. The problem is that some of the quests that you get from the Greybeards about learning a new shout word are in caves you already been in and you may need the claw again. Even some of the normal quests are in caves you've been before. So I highly suggest that you keep all the claws you get. It might also be a good idea to get back to Riverwood at some point and steal the golden claw. Just in case.