White spirits (aka mineral spirits on this side of the pond) will leave a bit of oily residue after it "drys". Surgical spirits (denatured alcohol) will evaporate more cleanly and is better as a rim cleaner.

My favorite rim cleaner is acetone. It is reasonably low in toxicity (use it outdoors anyway), evaporates completely and won't hurt the rims. I fully agree that steel wool is unnecessary and can be harmful to aluminum rims.