If it weren’t for the need for diplomatic relations with Spain, would there have been a problem with Henry putting a bastard prince on the throne?
She was the widow of Henry's brother, and the marriage required a Papal Bull (granted under pressure) to allow the marriage to take place at all. To then ask for an annulment.... well, that was a bit much for Rome.
Anyway ... one might speculate that Henry would not have married Catherine on his own; perhaps a male heir would have resulted from some different marriage, and the whole divorce thing might have been avoided.