I don't believe soaking in weak bleach would reliably dispose of anthrax spores. They're about the toughest pathogens in existence, and can survive in an oxygenated burial site for centuries.

Any reliable treatment (except maybe massive irradiation) would damage the skin beyond usability.

There are some types of bagpipe that use untanned skins, the Black Sea pipe (tulum) from Turkey is one. It's softened by soaking it in olive oil. I've never heard of an anthrax case from it.

Do we know where Norris got his skins from?