Maybe it's similar to a pierced ear. When you pierce it the first time, there's blood; but if you pierce it and immediately fill the hole(like with a piercing gun), there's no blood. Once you've had the piercing long enough, you can take it out and there won't be any bleeding.
Also, cuts with razor-sharp instruments can have little to no blood when the cut is initially made; when the blade 'fills' the hole that's made, maybe that stops the flow from ever making it out.
ALSO, if we can suspend enough disbelief to say that a guy was born with claws that shoot out from between his knuckles, maybe they're encased in a special channel within his arm/hand, that has tiny openings where the claws are meant to come out. When they are retracted, the opening just isn't visible; it stretches to allow for the claws when they come out!
Interesting conundrum.