It really depends if the coating has been worn-through or not. If not, you can clean off the aluminum oxide left by the other wheel. I'd suggest making a paste of Tartric acid aka Cream of Tarter, and using a kitchen sponge. Do wear gloves. This is pretty effective at removing black staining, which is AL-oxides. Being a powder, it is mildly abrasive, but less so than typical home cleaners like Ajax. As long as you don't use a power-tool, I don't think it would make the coating cloudy. Do be careful that the coating isn't compromise, otherwise you'll be introducing a corrosive compound into the coating where it will get trapped. Rinse well.
FWIW - I used cream of tarter paste on my flagpoles last week, which just had new sealants placed.It worked great, and made them look like new again. The dirt in that area is pretty corrosive, so that made the flagpoles turn dark after just 6 months.
2000 Ford E450 V10 VAN! 450,000+ miles
2014 ORV really big trailer
2015 Ford Focus ST