They've never counted illegitimate sons or daughters of a king as having a claim to the throne, or the Duke of Monmouth might have become king instead of James VII & II. Prince William and Prince Henry are descended through their mother from an illegitimate child of King Charles II, the older brother of Bonnie Prince Charlie's grandfather, so that should trump any claim this guy could make.
I believe that the Wittelsbachs of Bavaria have the best claim on strictly genealogical grounds, if the rule excluding Catholics were ignored.
Idi Amin once claimed to be the uncrowned King of Scotland, but I've never seen any genealogical evidence offered in support. Maybe he claims descent from the Black Douglas.
And what is your interest in all this? You sure know more than the average peasant.