If the prints are on the emulsion side, you're cactus. The shiny (base) side, can be cleaned by breath- fog and a microfibre cloth, while holding firmly flat on a neg- file (won't scratch), and polishing in gentle, small, circular motions, randomly, like you would clean a coated lens.
The fingerprints on the emulsion side, usually get eaten into by bacteria, creating a permanent pattern, though often careful re-washing in photoflo, and gentle cleaning with a fine sponge can improve things a bit.