I would. Or just water if he'll go for it. DD would likely take whichever was offered. If you did water and he was still not happy (milk and juice with the calories provide a more full feeling obviously) you could give him a small, ready made snack. DD loves to have a granola bar or a cup of cheerios or something like that when I need to buy time for a more proper meal or something of the sort. That could satisfy him enough, help you cut out dairy and give you time to get things ready.