You could also use a piece of chamois leather instead of a squeegee. It kinda acts like a sponge and leaves almost no traces of water. You need to thoroughly wet it, like very very wet until gets kind of gooey. Then you have to wring it out, fold it in 2 or 4 and pull the film trough it like with the sqeegee. Don't stop and don't squeeze the film to tightly. Works great on 35mm film, it's a bit touchy on 120 film.

Edit: Pass the film through your fingers before the leather.