Race question for curiosity purposes
I think you can use the popular catch all self-identify which means:
To believe or assert that one belongs to a certain group or class
(American Heritage Dictionary)
There is a person who "self-identifies" as black despite being of non-black descent. Wikipedia article on her is here.
So you could say you "self-identify" as black. Alternatively, you could describe yourself simply as "envious" of features of a particular race (or culture).