If it's small enough to fit in a plastic tub you can use electrolysis. Minimially you'll need a small transformer or battery charger. I was able to accomplish this with an old transformer from printer in about 24 hours. It's a lot quicker and more effective with a regular battery charger but the one I have is electronic and you can't force it to work if it thinks it's not charging something. There is more amps and volts, you can really get it cooking.
The top of the ball where it's really shiny I did manually beforehand. I stopped at this point but if you do it long enough you can get it looking like new.