Apologies for not replying earlier. From my perspective it's not the spelling of the word wiz. It's the phrasing.
Computer wiz: No negative connotations. Computer wizard is implied.
Wiz kid: Also fine. Wiz is an adjective implying competence or intelligence.
Take a wiz: Now the meaning of wiz has changed because wiz is the action.
Wiz at home: It's easy to read wiz in this context as an action one is doing, which is why I say it is the phrasing rather than the spelling.
> We did talk to a branding guy rather informally. He mentioned the chance of misinterpretation, but that the chance is very very small.
In the right context this person is right. Used as noun or adjective its unlikely people will misconstrue the meaning. When it is easy to unintentionally interpret the use of wiz as an adverb or verb it becomes much easier to misconstrue the meaning.