You click the Black box then it actually asks you to describe what "type" of Black you are haha i.e. African-American, Afro-Caribbean, African. So while I don't think that schools make a distinction between the different sub-sets, you can choose from one of those. Same with Hispanic or Latino, it then lets you pick the type.
OP, you wouldn't be the first person to try and do this and you wouldn't be the last. I agree with what NickNaylor said about self-identification. If you have identified as "African" and not "South Asian" your entire life then you should put it down. I had a friend who was from Kenya who was of Indian descent and she was in the African Student Association, always repped Kenya for the cultural shows and everything. She still identified as Indian, but she identified as African as well.
It's a personal choice and it's one that you should be prepared to potentially defend if necessary. Also, I wouldn't put it down now if you haven't put it down in the past. If you didn't put Black/African-American when applying to college or the census or any of the other places you can put it, then now is not the time. If you identify as African, you should have been identifying as it for a while now lol.