In England, I believe that Roger Manners, 5th Earl of Rutland would become king; I could be wrong, but by that time I think that he was the senior male descendant of the Yorkists through Edward IV's older sister Anne.
In Scotland, James Hamilton, 3rd Earl of Arran should become king, but given his insanity he might be passed over for his brother John (IOTL the first Marquess of Hamilton).
Don't think anyone is cracking open the genealogies to find the senior most heir - will be more a case of who is the most powerful or good at horse trading. In any case, the senior male descendant of the Yorkists would be
Duke of Clarence's Pole descendants, who are apparently bouncing around Italy at this point (though obviously there's the claim that Clarence's descendants lost their claim through his attainder)?
When you're going so many several generations, basically everyone has some drop of royal blood and can come up with some plausible claim - there's not really an obvious 'legitimate' pick and some of most convincing potential claimants
on paper are probably off the table (Clarence's male-line Pole descendants, absent in Italy and Catholic; the Staffords, with their eclectic mix of royal blood, having been much diminished since the execution of the 3rd Duke of Buckingham in 1521; the Nevilles, arguably the rightful domestic Lancastrian claimant by virtue of their descent from Anne Holland, granddaughter of
Elizabeth of Lancaster, having been exiled after the 1569 Northern Rising and Catholic).
Earlier on the Lennox Stewarts did maintain an alternate claim on the basis of the 1st Earl of Arran's complicated marital history rendering his descendants (allegedly) illegitimate - the Lennox Stewarts being descended from the 1st Earl of Arran's sister. Don't know if
Ludovic Stewart is inclined to have a go at the throne, or if he'd get anywhere if he tried?