Oh, the finger prints on a proof coin!
The sad truth is, there is no way to remove them without risking damage. If you lucky you may be able to use dish soap and water with a light finger rub to remove them, but there is still a chance of micro--cratches. Dry it with a micro fiber cloth by patting it dry, gentally.
I wouldn't use any kind of cleaner fo fear of dulling the finish.
The best advice i can give you is not to drive take photos of things and upload those photos onto the net whilst driving you mentalist, it spoils the picture quality.
For proof coins - if the finger prints are recent and have not affected the polished surface of the coin you are in luck, soak a cotton swab in acetone (not nail polish remover) wipe off the finger print and air dry - do it as gently as you can without applying too much pressure, let the acetone do the work.
If the finger print is old and has affected (corroded) the polished surfaces - there is no bringing it back - any attempt at polishing will leave marks on the coin and in most cases make it worse.
