If lessons are not going to happen, he can watch how-to-ski youtube videos for beginners. There are many.
Fearless, athletic, strong and fit beginners can have a blast without lessons. On icy New England groomers (blue ones, not to mention black ones) they are a danger to themselves and others, but that doesn't cut out their fun if adrenaline rushes float their boat. What happens with these beginners is they use trial and error and find something that works down on the easy terrain. Then they lock onto that, repeating and exaggerating it all over the mountain. The problem with this is that what trial and error produces is almost always a dead-end technique that will fail when speed increases on blue terrain. The black groomers that he longs to ski will simply bring out the weaknesses of his technique quicker, before he gains speed. Blues can be more dangerous than blacks because confidence allows the fearless to go fast before something bad happens. When it does, they are smashing into others below them or into the trees. Someone mentioned hockey stops; yes, teach him to do those. But you already know on icy man-made snow those hockey stops take a while to stop you.
If he watches videos beforehand, takes what the instructors are saying seriously, imagines making those turns in his mind's eye frequently before hitting the snow (visualization is really helpful), then he will have a chance of getting onto blues and blacks and not hurting himself and others by skidding down out of control. A lesson would be better. Watching videos and taking a lesson would be the best of all.
SNUG (aka tight) boots are going to be very, very helpful, as already suggested above. If you can get him in boots that have no slop, that are difficult to wedge his feet into, that threaten to hurt -- until he stands up in them for a while and realizes they are OK, then he'll have more control over his skis and learn a lot faster.
Enjoy your vacation! Watch those instructional videos together and enjoy the stoke.