I have used acetone to remove the sticky residue from the coins. In my case they were low value Indian Cents, but this should work with silver or gold coins just as well. This does not hurt the coin surface if done properly. If acetone doesn't work, you can also try paint thinner.
Acetone is a flammable liquid. Use in a well ventilated area, no smoking, keep out of reach of children, etc.
What you will want to do is to pour some of the solvent into a glass jar that has a lid, and put the coins in to soak for at a couple of hours - with the lid on. The residue should dissolve into the acetone or turn into a "goo" that you can then wipe off with a piece of soft cloth. It should come right off without rubbing. If it doesn't either soak longer or try a different solvent. Try one or two coins first before you dump the whole bunch in.
Rinse the coins in a little bit more clean solvent, then allow them to dry. There is no need to rub the coins dry -- the solvent will simply evaporate. This will also remove any grease that has deposited itself on the surface. So you may find that they have a "dry" look to them.