[Uncle Bulgaria]

For chassis with a bit of rust, and for car parts, tools, bicycles, watch elements etc. I recommend common white vinegar. It's an excellent and cheap de-ruster. It can bring back really unsightly things to clean metal. For more delicate items, strong tea works well. They both chemically deal with the rust and aren't so aggressive that they affect other components or elements. Just wash off or neutralise with a bicarbonate of soda solution afterwards. It sounds like you don't need to do this as it's minor cosmetic rust, and as others have said it won't spread in its current environment.