Shifting doesn't require any specific body parts, but i imagine the lack of one may affect your shifting depending upon your shifter type.
A razorclaw shifter wild shaped into a form without arms wouldn't gain his claw attacks, but would receive the other benefits of shifting (+2 Strength, any shifter feats he had), for example. The same would be true if that same razorclaw shifter was in the form of a bear; the bear already has claws, so he probably couldn't grow claws while shifting. (Or, he would simply use the more damaging of the two claw types, his or the bear's.)
Note, none of this is explicitly stated anywhere in the rules; it's simply how i would rule it. The rules on shifting while polymorphed are dreadfully thin (read: nonexistant).