Don't know your rim material of what is on them so this is all I can say if they are aluminum of older chromed steel and not carbon. If I remember my time in Australia white spirit is srtong stuff for hands and lungs so cautions like gloves, don't breath fumes, etc.
Surgical would do the job, perhaps slowly but be safer. Steel wool #0000 we use over here will work on minor rust and polish up the rims.
I use surgical frequently on my aluminum rims to keep them looking good and the brake track clean. I use Mothers Mag & Aluminum Polish and Simichrome for chrome to remove any stains and polish.
My MTB rims get really ugly and I would use soap and water followed by Mothers, no spirits or wool.