https://support.google.com/a/answer/6214622?hl=en#zippy=%2Coption-dns seems to show ways to implement this (via https://www.reddit.com/r/k12sysadmin/comments/10rwtrr/problems_with_youtube/): either DNS fiddling or http header fiddling.
I'd think of the second option in this case.
Does this sound reasonable?