To finish metals, I often use wet/dry sandpaper. The finest grit that I have on hand is 2000. That seems to me to be fine enough for metals; I don’t really want a mirror finish. But when I have tried to put a shine on Delrin, 2000 grit leaves the surface dull and unattractive.
Recently I ordered some pen turning blanks in order to have stabilized hardwood to make reel knobs. From Craft Supplies USA I also bought a pen blank of a plastic that they call “Alternative Ivory”. Before finishing the order, I noticed a “Micro Surface Pen Finishing Kit”. This is a set of 9 foam pads with abrasive faces, and the grits range from 1500 to 12000.
I made an Alternative Ivory knob and used the kit to finish it. By the time I got to 8000 grit, there was a pretty good shine.
So I then tried sanding a small piece of black Delrin, and that also worked well.