Slerk, fingerprints such as the ones on your coin cannot be removed. Acidic oils in the fingerprints have chemically reacted with the surface metal of the coin, and they are now permanent. If I am incorrect and you find a way to remove them without damaging the coin, please let me know. I have a 1909 VDB
Lincoln Wheat cent that would benefit from this treatment.

Inordinately fascinated by bits of metal with strange markings and figures