The Christmas Song (Chestnuts Roasting On An Open Fire) will feature on the special edition of his Kisses on the Bottom album Complete Kisses.
It was performed as part of a concert at Capitol Studios in Los Angeles that will be aired this weekend on ITV in the UK.
"Doing Chestnuts was a bit intimidating because when you do these old songs, there's so many good versions of them - particularly Nat King Cole's in this case," McCartney told NME.
"So, I thought, 'You know what, I'm not even going to listen to it, I'm not going to see who's done it, I'm not even going to figure out how I'm going to sing it'. So it was just done in one afternoon in New York. And I'm quite pleased with it, because it's not like anyone else's version."
The Capitol concert was the first time the Beatles legend has performed an entire show without playing an instrument.
"It was a bit naked," he said. "You never realise how much your guitar or piano is protection. There's something between you and the sound. Like you're plugged into the music, because you've got your hands on the keys, or you've got your hands on the fret.
"When you haven't got anything, it's like - what do you do with your hands? They feel very awkward.
"So there was a bit of hand waving here or there, but that was it. No mic techniques. No [Roger] Daltrey swirling."
The Capitol performance is available on Complete Kisses. It will air after The X Factor on Saturday 24 November.