With Henry VII losing both of his sons, he’ll make arrangements so that his daughter Margaret becomes Queen without shenanigans (Buckingham or anyone else trying to pull either a Stephen or Richard III will have to contend with James IV). James IV will be content with having no formal power as King Consort since he’ll need to be in Edinburgh to keep the Scottish nobles from getting any ideas. Besides should the English give him or Margaret any trouble, he has the trump card of being the father of the next heir to the throne (TTL James V / I)