Now I'm beginning to feel ethnically-deprived, being only German all the way back to grandparents on both sides. Oh well, one can't have everything, right?
As far as Kurt's skin color, maybe they originally chose white just because he's from a European background and his features are essentially Caucasian, so that's the likeliest possibility. However, I do think he'd have been better portrayed with a seriously darker complexion. After all, being blue, he is really a "person of color", in the current terminology. (Yeah, white's a color, but that's not the point.)
What may be more relevant is the image Kurt himself chose to present, via the image inducer. The writers could have made it anything, but they overwhelmingly had him being white and handsome, often in the image of Errol Flynn. What an opportunity they missed, when he could have been shown to vary himself through many other possibilities, even female!
I also don't think it makes any sense to show what he "would have been" without the mutation. Rogue should have taken only his powers, not his appearance. Unlike most other mutants (at least at that time), he was born that way. Maybe there is no other way he could have looked.