Help with removing finger print in paint

Been there, done that.

You could try your idea; I don't know if the oils from your finger skin might not allow the new coat of paint to stick properly.

Would polishing with a dry cloth, say a clean T-shirt do it?

Been there and done that.  Now I wear vinyl gloves when I paint.

Using very fine paper like 1000 grit, it will take quite a bit of sanding before you get into the molded plastic and start destroying detail.  Just keep checking visually every few strokes. I have sanded out finger prints.  Also, you don't need a very heavy coat of paint to cover up what is left of the finish, so the further paint doesn't do much to harm the detail.