Yes. Each fresh bath helps reduce contaminants. I used to put a few drops of the used acetone on a piece of glass and let it dry. It helped me judge the progress after each batch. I never cared for pat drying. Lint will be left behind. With proofs, that's really bad. It's a spot waiting to happen.
Soak in acetone, rinse with distilled water, and prop the coin up on a blotter of some sort (paper towel) but heavens 'no!' with the dabbing, wiping...........