I have used vinegar for rust removal.
Normal groseery store pickling vinegar (10% Acetic acid) will do very well, needs hour or two in 60C or overnight on 20C or three days in 5C temperatures (It's autumn here and I dunk them outside, or I get hungry).
When you pick them up from the windegar they liike like nothing has happened...but they feel really dirty and slimey, nylon brush will sort that out. You may want to wear whatever kichen/exam gloves. You need to wash neutralize the acid right after, normal soap and wrma water will do.
If you like them grey steel matte coloring, a half an hour into warm phosphorous accid (Tea kettle limescale remover) will do that, and wash/neuralize with mild soap, I use hot water, dry right after and oil. pretty nice.
If you need shine.....then you need to know material.
For historic show piece I prefer rusty. Maybe you have more of them and treat them differenty and then put all your balls into display

Would give someone somthening to wonder. And you could explain that they all same just treated differently. Old rust, new rust, vinegar pickled, phosphated, lisnished, tumbler finished....
Pekka