Well, Henry (if Catherine dies instead of James) is going to hate the Scots almost as much James V hated the English. I don't think even his sister being the consort of their king is gonna save them from a possible Edward Longshanks invasion.
That said, Henry doesn't have a male heir, so he's probably gonna start fishing around for princesses in any anti-French powers - like Austria-Spain-Burgundy. Portugal's infantas are too young at the time of Flodden. The same goes for the king of Denmark's cousin, the kings of Poland and Hungary's daughters. Navarrese princesses are thick on the ground, but might be seen as too French. Bona Sforza might be an interesting match, or a Neapolitan princess if Austria-Spain-Burgundy's are unavailable.