I soak my rusty parts (including nickel plated parts like handwheels, slide plates, etc) in Evaporust.
In fact, I soak just about everything in Evaporust even if it's not rusty. It floats away even hardened oil/lint/gunk overnight and they're clean - ready to polish and put back in place.
It's safe for plated surfaces and non-toxic. It's cheap and reuseable until it turns black. You can find it at auto parts stores. :)