There's ZERO reason to soak the snake or spray it down with anything.
All you need to do is use bedding spray or PAM as directed, nix head lice shampoo works but isn't necessary at all.

Spraying the tub and the paper towels and allowing them to dry is all you need to do to treat.
Well that and spraying the surrounding area, I'm not sure why you are spraying anything on the snake, especially permethrin which IMO should never be done.