For years I've use Ospho/phosporic acid all the time to neutralize rust on parts. It won't harm surrounding finish and gets rid of the rust. It doesn't burn your skin like you think it might. I use a q-tip and dip it in the bottle then lightly dab on rusted bolts, screws and parts.
https://www.acehardware.com/departments/home-and-decor/cleaning-and-disinfectants/rust-removers/1386...
https://www.acehardware.com/departments/home-and-decor/cleaning-and-disinfectants/rust-removers/1386...