I do this with my newer jewelry pieces.
Sand with varying grits of sandpaper, starting with rough grits and working your way up to very fine grits. It doesn't take much time with each grit, and you'll get the hang of it after doing it a few times. Always use wet/dry sandpaper and keep it wet to avoid breathing the polymer dust (and to avoid having it all over your work area!). Once the piece is satiny smooth, buff it with a soft cloth (like an old white tee shirt or a piece of old, soft white denim - colored cloth can discolor your polymer) for a less shiny finish, or a dremel tool with an unstitched musllin buffing wheel for a very shiny finish.
It takes time, especially on a round item, but the finish is amazing and won't discolor or come off.
Once I get into my studio, I'll add details about what sandpaper grits I use.