This is a toughie and I'm afraid I cannot find the answer. All I have been able to find out is that it was written by Adolphe Adam, and the film tracks were orchestrated by Herbert W Spencer and the music score is by John Williams.
Perhaps they used session musicians and singers although it sounds like an established choir in which case they must have a name. Good luck with your search.It is my favourite carol and this is a lovely sweet version of it, so I will be interested to see if someone knows the answer.