If OTL is followed, Elizabeth of York will have another child, then die of complications from the pregnancy. Henry VII will then have to remarry. I think that marrying Catherine of Aragon is a very real possibility. Henry VIII was able to get Papal approval, and the alliance is still important for both Spain and England.
If Henry VII and Catherine have any surviving male children, then that is going to necessitate a regency for the child (I'm a supporter of naming the kid Edward). Let's say the marriage takes place in 1504, on the heels of Elizabeth's death. Edward is born in 1505, and Henry VII dies in 1507 (supposedly for exerting himself).
With Catherine as the Queen Mother and regent the king would probably be deeply Catholic. The Reformation in England would be completely changed. However, given her OTL example, she and Henry VII would need a lot of luck to have a surviving child.
I still prefer the idea of the OTL facts repeating ITTL, and make the child of Henry and Catharine (if any of them survives) be a daughter, just to see the chaos that would create.