As mentioned above, it wasn't necessary a wholesale new religion. Yes, as you mentioned, the Henrican Church did swing between periods of reform and conservatism, but the Henrican Church didn't really make any wholesale doctrinal changes. The Articles in 1536 were semi-Lutheran, with the alteration of minor feast days into working days: mostly for economic reasons. The English Church didn't really become "Protestant" until Edward VI and Elizabeth's reigns. Henry's main attack upon the church, the dissolution of the monasteries, wasn't exactly unwelcome. There had been attacks upon the monasteries for years because of the idle lives and the supposed vice within them, and of course the secular powers (and the crown) benefitted from the dissolution. By 1538, the church began to drift back into a more conservative direction, and Henry VIII's religious views certainly weren't that radical. He remained essentially a Catholic, but with the belief that he was the head of the church.If Henry can force the country to accept an entirely new religion, he can have his wife executed. The big obstacle to doing so would be the prospect of becoming an international pariah rather than domestic opposition.
Nothing is stopping him from executing his wife; but there will be consequences for doing so, and more consequences than he faced for executing Anne Boleyn and Catherine Howard, who were native Englishwomen.