Steering wheels get a lot of wear plus they have quite a build up of hand oils on them......both contribute to the difficulty of getting anything to stick. The typical dyes work of non wearing plastic surfaces made from abs or vinyl but it is coubtful that it would last on a steering wheel.

Why not contact one of the outfits that restore steering wheels and ask how they process color changes? OR, there must be a source for replacement wheels if you are going to change to a relatively common color....or go with a black wheel like they do now....matches everything and doesn't show dirt.