Agreed. I’m not sure why the term’s age means that it must be the ‘cheer’ version. Either is possible, but ‘what’cha up to’ sounds more natural because ‘cheer’ does not have a ‘cha’ sound.
(In case anyone is unaware, the final consonant of ‘what’ and the initial consonant of ‘you’ usually mix into a ‘ch’ sound in spoken Southern British English. I presume everyone understands that, but just in case, you know!)
How about a cite that the expression “What are you up to?” was used 300 years ago? Sounds very unlikely to me - that’s would seem to be a modern expression, unlike “What cheer.” I can’t recall seeing “What are you up to,” or anything similar, in Defoe, Dickens, or any other pre-20th century author.
I’m not sure how this is relevant at all, since the expression under discussion in the OP is “wotcher,” not “wha’cha.” If anything, it is an argument against a derivation of “wotcher” from an expression beginning with “what you.”