^^ this
I probably wouldn’t even try it for “internal” (cup) rings.
If I really insisted on trying to polish the rims of an SS yoyo (which I probably won’t), I would not only mask, but I would also put the yoyo half in the chuck of a drill, taking a bunch of precautions (mostly against torque; you could strip your halves in a hurry if you do something wrong). Even though the yoyo half would be spinning pretty quickly, you could use a jig or at least a support for your hand to make your aim a lot steadier as you start applying the abrasive/polish.