He should be fine. Keep an eye on his BMs and take note if he mentions he has a sore tummy or anything. But if he is already having it in other way (on his cereal etc) then he should be fine. If he does have a tummy reaction to drinking the straight milk, try rice or oat milk instead. If he is still BF then you don't need to be concerned about it being a 'whole milk product for children under 3 or 5'.
He doesn't need it though, if he doesn't like it, water will suffice while he is at CC.

Both my girls can eat milk on cereal, yoghurt, cheese, ice cream, but if they drink cows milk or eat too much cheese, they end up with sore tummies and very soft BM, so they drink rice, oat and almond milk instead.

HTH