Ummm, I wet my sponges with stabilzer to wipe the film down. Wetting with water will dilute the stabilzer by a fair amount.
PE, I was instructing on how to clean the sponges before using them for b/w film. I always rinse out my sponges before use as it softens them up. Then I dip the sponges in photoflo (for b/w) or final rinse/stabilizer (for various color) then wring them out and wipe the film. The only moisture on the sponges at the time of wiping the film is the appropriate "final rinse". Since I use the same set of sponges for all film, I rinse them out thoroughly before each use.