Being into RC car building and modeling, I can tell you that removing deep scratches can be a time consuming job using sanding papers from fine to super fine (2000 grit) with wet sanding at the end for the best finish.
Painting over the prepared surface will work well of you use a fine plastic primer and them acrylic spray paints. E.g. Tamiya fine white primer and Tamiya TS paints. Beware, it's easy to botch a paint job, so try it out on some scrap plastic first and read tutorials on the web.
But what matters most: Have some fun with your Duo playing games!