> Baryon number, lepton number, strangeness ... all lost.

Even for classical black holes I don't think that's the consensus among physicists. The general assumption seems to be that quantum numbers are still conserved when you throw stuff into black holes, just like electrical charge.

Now, as for Hawking radiation, it's worth pointing out that Hawking's calculation only works for large black holes (low curvature near the event horizon). Once a large BH has shrunken down to a tiny BH (-> high curvature at the event horizon), the calculation no longer works and it is unclear what will happen. Some people say the BH will evaporate completely, some say there will be a remnant – who knows. (Both solutions have their issues.)

All in all, I'm skeptical of the "shaving" you describe.