I have had good results with orange degreasers and if you get to the point of wanting to use steel wool, try using a citrus based hand cleaner that has pumice in it first. The pumice citrus ones work really well and don't scratch much at all. I would say not at all, but if you try hard enough it will scratch. Just squirt some on your finger and rub lightly.
I started out trying to use this for tar but is much better for the goldish stains. Also really helps break up the gunk on barrels. With rims in extremely poor condition, a polish step really will be needed anyway after extreme cleaning.