In spite of various warnings to the contrary I routinely clean negatives with brushes and even an antistatic cloth and have NEVER scratched one with either. You have to be more careful with the cloth. If you're really scratching them with a brush something is wrong.
Modern films are factory hardened and really shouldn't need a hardening fixer, but I use it anyway for film. I use Kodak Rapid Fixer, mix per instructions (including the part B which is the hardener) for film, same strength minus the hardener for paper. But I've used non hardening fixer and still can't imagine scratching a negative with a brush. I'd echo the suspicion that you are getting the scratches somewhere else.
Wet film is very, very soft, especially as it starts to dry. As the poster above, I'd never use a squeegee on wet film, ever. It's best to use nothing to wipe it with, just wetting agent and hang up (and, like others said, not too strong - no more than half recommended strength) but I have rinsed my fingers well with water and gently run a roll between two wet fingers to get most of the water off, without ever scratching the film. If you had something gritty on your hands that could be disastrous though so the advice above about not doing it is the safer approach.
One problem with wetting agent is that it should really never get on your reels. Over time it will make them sticky and hard to load (plastic reels, which I use - probably not good for stainless either but easier to clean off, I'd think.) I remove the film from the reel and gently place in a wetting agent bath. One has to be careful when doing this, though.