Personally, I find 220, even 320 grit to be a little to course to just remove paint. I would start with 400 wet, then 600 wet. From there I switch to polishing pads by Micro Mesh. 4,600, 6,000m, 8,000, & 12,000. All are used wet. Clean with a tack cloth, then repaint.
You also need to figure out how your finger print got into the paint, and how to prevent that from happening moving forward. You should also be wearing either a latex or white cotton glove when handling a painted or being painted model.
Joel