AFAIK the only correct AE spelling of the word, in whatever context, is 'whiz.' However, 'whizz' seems to be an accepted BE spelling.
But beyond those two, I think we should draw the line. LEO doesn't really need to list common misspellings as variants, since it has the handy algorithm that points users to similar words anyway.
In particular, I would strongly advise against *'wizz,' which is exactly the kind of misspelling perpetrated by people who can't (or can't be bothered to) distinguish phonetically between minimal pairs such as which/witch, whether/weather, or where/wear. Granted, there are a lot of them out there, but they shouldn't be allowed to influence dictionaries. The sound /hw/ is really not that hard to make, and there's no reason to discard it, since it serves a useful function in the language.