Since this is a small object it is very easy to remove rust chemically. Citric acid removes rust very well and boiling solution of citric acid in water removes rust really well and also very quickly ;). You can get citric acid powder in grocery stores and it is quite cheap. It's OK, to use quite a lot of it. You can mix something like half citric acid powder half water by volume, but if you want you could use less and it will still work only a bit slower. I have used a simple kitchen pot to clean small metal objects successfully. It does not seem to damage steel.
Keep in mind while it''s not the strongest and most toxic acid, it is still a hot concentrated acid so it wouldn't be fun if it gets in your eyes or on your skin. Also I wouldn't boil it too hot since the citric acid itself will boil at 175 degrees C and I don't think its vapour is fun to breathe or if it gets in your eyes...
Iron citrate is produced in the reaction. It is black and can be hard to wash off clothes and other stuff, but you can wash it off from the metal with soap and water. I wouldn't eat the stuff, but as far as I understand, it isn't very toxic. The surface will not be shiny and may look greyish after the process and I find it to be easiest to use metal brush bit for a rotary tool to finish cleaning it and make the surface nice and shiny.
I haven't tried it, but I think the solution could be kept for later use as well.
This works on other corroded metals like copper(and copper is the stuff that usually corrodes in silver jewellery) and aluminium as well.