As you can see, the poor thing has had some careless fingers laid upon it at some point. Does anyone know a way to remove the prints without taking a chance of scratching or damaging the finish, or should I just leave it alone?
Acetone will remove recent fingerprints and smears without otherwise altering the surface. If they have been there for a long time a shadow print will be etched into the surface.
Don't steal your wife's nail polish remover. She will spit in your food and it's got dye and other impurites. Use the pure stuff sold as paint thinner at the hardware store. Just a quick dip is all you need and allow the acetone to evaporate. No need to be scrubbing at your coins and no need for soaking. Acetone vanishes very quickly on exposure to the air so those who try soaking their coins use a helluva lot of the stuff and if it hasn't removed the marks after a ten second dip it's unlikely to change after an hour.
Non illegitimis carborundum est. Excellent advice for all coins.
Make Numismatics Great Again!
DON'T! It's better to have fingerprints than a cleaned proof, any day. If the prints bother you, get rid of the coin, as is, and get yourself one without fingerprints.