Oh oh oh I think this was the one!

That kind of whistling sound. That's what I heard.

"'Twas The Night Before Christmas"

The Harry Simeone chorale

https://youtube.com/watch?v=fEijZQZ5OwI&si=-6ls1PWa4n20XH_S

Thank you commenter on the 1942 version of this other one which is very similar. 

'Twas The Night Before Christmas - Fred Waring and The Pennsylvanians -1942

https://youtube.com/watch?v=dPPltRf2tfo&si=BTdq-xT7kiJFiJxx