I color at home, so the dye formulas I'm sure are different, but my dd's oxy wipes get it off. It probably has similar ingredients to the rubbing alcohol/witch hazel.
I put a thin layer of petroleum jelly around my skin right by the hairline and on my ears, that way it gets on that, then wipes off easily w/ a wet towel I keep handy while applying the color. But sometimes I get it on my chest or arms, and the oxy works great.
Getting it off the walls is a whole other story. Mental note to self...full force allergy sneeze with hair dye in a light colored bathroom = spending the weekend repainting the bathroom