So far as I've seen and tested in the past, Sonic's coloration of his fur is a tint that's also applied to his shoes... so whatever shoes he's wearing, that is the tint he'll have (i.e. gold-ring costume = yellow shoes = yellow tint; green cuff costume = green shoes = green tint, etc.).
Wait... this gives me an idea. We can change the color of the shoes, right? (Not normal texture, I mean the effect texture that gives the running blur) Would changing that also change the tint?
But why is Sonic blue and not a redish blue normally... hmmm....