Baby powder or corn starch will remove fingerprints. I haven't had one on black for a long time, so experiment first. Unseal is my favorite, but I no longer have any of that.
With baby powder, I will gently rub with a rag, then blow with the air compressor. I may need to use a damp cloth to finish, especially on dark colors.
Yes, it is easier to just start over, but not always that easy. Especially if you don't have another mat the color you need, due date is now and delivery is in a couple days.