If history is anything to go by it would either be his mother (like in the case of Edward III, although Isabella was a royal in her own right, even if it wasn’t to the English throne) or the next in line to throne (like Edward V). Both of those cases didn’t turn out great though and I think Catherine and Harry wouldn’t inflict that upon themselves.
He would most likely have a regency council, like Edward VI, which would probably contain Catherine, Harry, Edward, Anne and maybe one of the York girls as advisors and to do events upon his behalf.