On the last part that with heavily rusted tip, usually I used finer 1000 grit sand paper, and only used hand/fingers holding the paper when rubbing the tip, as its more controlled on the pressure and angle. Rubbing the tip on the paper that placed on flat surface like sharpening a knife usually ended up unevenly cleaned surface.
Once done, buffed with metal polish like Brasso and then thoroughly clean the polish residue like using acetone or IPA.