Why I'm hesitant: Superheroes are designed so that in two or three sentences, you can basically communicate their backstory, motivation, and struggles.
Examples: A philandering, millionaire, military arms developer gets critically by an evil organization wielding his weapons. To save his life, he creates a super-suit that not only keeps his heart beating, but also fights crime. (Iron Man.)
Four scientists are in space when blasted by radiation that causes them to mutate horribly, but with useful side-effects. Thrust uncomfortably into the public spotlight, they have to deal with both their new and strange reality, and many disasters that they may be able to solve. (Fantastic Four.)
Young, disaffected teenagers suddenly experience strange mutations, which often bend the laws of nature. Faced with scorn from normal humans, these teenagers divide into two camps, the separatists who often attack normal human infrastructure, and those who attempt to prevent these attacks. (X-Men.)
Notice that these descriptions play on your standard stereotypes. While there's no reason that the first guy be white, or straight, or male, the stereotype is that he is. For all the character depth that goes into him, remember that you can always boil it back down to those sentences. Comic book characters are designed that way--your stereotypes are affirmed, simply because it makes it easier to get past the backstory and on to the real plot. Now, for the man in question,
A young nerd, still in school, is exposed to spider venom that dramatically changes his physiology for the better. Though he initially fails to use these changes for good, he quickly learns his lesson when his Uncle is killed. Now he fights crime and injustice, despite the havoc that it wreaks on his personal life, and struggles to live with the consequences.
If we add the black part in, we've got lots more to consider, beyond the stereotype-breaking. For example: Believe it or not, people are racist. If a black man doesn't show up for work, they assume he's being negligent. In this case, he's fighting crime, which makes the point moot, but this is definitely a misconception that's going to pop up. Which can definitely make for good drama, yes, but the tendency will be for heavy-handed messages about racism. There are more factors to consider: What do people say about a down-on-his-luck black dude versus a white dude in the same position? What happens when he doesn't show up for a date--is the assumption going to be that he's cheating on the girl, which is clearly out of character? How does he deal with this racism? Is some part of the audience going to assume he was living on the streets once, and that's how he can fight? Are they right?
Now, these aren't all huge problems in and of themselves. But they complicate the character, probably so I can't summarize him in a few sentences. And that's a big part of the comic-book appeal, for me--despite the depth, the development, we can always come back to the same core character. It's a world painted in bright colors, with broad strokes, which means it's not always realistic at times--more like a vaudeville play, or a Saturday morning cartoon. But when I want to read/watch comic things, that's what I'm expecting, and I think that's what the target audience is expecting. That's why I'd be really, really wary of a change like this.
There are other superheroes that I wouldn't bat an eye at people turning black. And if someone wanted to come up with an erudite, black comic-book character, that would be more than fine. But realize that race is going to have to be woven in from the beginning, because of these sort of complications. It's not fair, yes, it's racist, yes, but this is more the fault of the (modern) society that the character must interact with than the writers being biased. But maybe I'm wrong, and I'll allow for that--it could be that the writers will write something that makes Moby Dick look like a hack job.