Yep, Wally’s skin is black, just like all polar bears. His fur is clear, and his skin is black, yet polar bears appear bright white due to the reflection of light off their hollow hairs.
I don’t think Wally shaving for no apparent reason is even the insane issue here, it’s the fact that he used one of those old-fashioned barber straight-edge razors. Those things are terrifying. When I first started shaving I did so with an electric razor, it was a while till I even used a normal razor. But those straight-edge ones, who thought that was a good idea? Maybe it was rough times for barbers back then and they used them to defend themselves and have knife fights in the back alley.
Perhaps those were the same razors they used for blood-letting, if you’ve ever seen the rotating red and white tubes at a barber shop, that’s what it is symbolic for. Back in the days a barber was a jack of all trades, he’d pull a tooth, stitch a wound, give you a nice hair trim and you’d be on your way.