If you get a nice metal one you can use acid to dissolve the hair that gets stuck in it. Then you can just wash the soap scum off.

DISCLAIMER: acid is incredibly dangerous. Make sure you know how to handle it. Wear easy to remove protective clothing, acid-rated eye protection, acid-proof gloves, and ideally do this outside, where spills aren’t a catastrophe.

I don’t do this to clean my snake, myself, but I do sometimes use sulphuric acid in my drain to clear up clogs my snake can’t reach (note: my drains are safe for this, not all are. Do not just assume you can dump acid down the drain and be done with it. You can corrode or rupture your waste lines.) so I know it works fine to break down hair and stuff, then the rest just washes away. If you go this route, soak in acid outside (it fumes, and you don’t want to breathe it), preferably in some sort of sealed container. But do make sure the container is acid-proof, like glass. And you can dilute the acid if you want, a little goes a long way if you let it sit for a while.