Only Christmas Carol Beatles recorded?

On their first fan club Christmas Record (1963), The Beatles quote various secular Christmas songs: Rudolf, Jingle Bells, etc. But a single Czech Christmas carol forms the theme: 

Of course, all their variants on Good King Wenceslaus are parodic. They also perform it as a pub sing-along

In fact, the carol -  often announced as moral lesson about the importance of altruism - arises out of bloody historical events. The real Wenceslaus was a teenager murdered by his half-brother, probably with the connivance of his mother - see here