I'm not so sure on that point. After all, there are plenty of examples (even today) of members of the Royal Family choosing not to use the highest title they have; the Duchess of Cornwall, Viscount Severn and Lady Louise Mountbatten-Windsor, the Earl of Dumbarton etc. Either way, for the sake of this TL I think it's easier to follow if I refer to him as Duke of York until he becomes King as there are a lot of 'C' Dukes which could be easy to lose track of!He can refute the Prince Regent title (and maybe would never created as Prince of Wales) BUT Cornwall is his own highest title and need to be acknowledged so his style must become Duke of Cornwall and York
I would say though, he isn't refuting any title. For example, he is Prince Regent, he's simply elected not to be styled that way at court.