If I get a lot of gunk on the rims (fresh tar, over-spray from waxing the chain, etc.) that doesn't come off, I'll use a diluted down degreaser (purple power or such), followed by car wash and warm water.
Most tire shine products have a specific warning on the can not to apply to motorcycle or motorsport tires. I'm assuming there is a problem with compromising traction. Don't use Spray Nine, either. Lots of folks like it on tires, but it actually dries out the rubber.