What a lovely response you made to your son's request! Let me suggest a few other things to help the next time something like this happens and it will probably happen many times over the next few years.
Acknowledge the legitimacy of your son's feelings. ("I can see that you want to be just like your dad!") That way he won't feel you're rejecting his request (and him) out of hand.
Also, don't assume that when he says he wants to look like his father, that he is only talking about skin color. Young boys identify strongly with their fathers. "Looking" like him can really mean that he wants to be bigger, stronger, and more powerful. You can even explore those issues with him. ("It sounds as if you want to be big and strong so that you can do lots of stuff!")