Age restrictions and hunters safety certification will be the obstacles of concern. Montana is still age twelve although I seem to recall some special exceptions in recent years but only for residents I think.
So, he will skip school for a week or two? Not sure that sets a good precedent.
Consider taking him to Africa to hunt. I'm not kidding. No age restrictions or safety certification. And he wouldn't have to miss school because winter hunting there is during our summer. The lodges often run special deals for father-son packages. Right now my lodge has a special deal four days hunting and four animals for $2400 (blesbuck, impala, wildebeest, and springbuck). The hard part would be stopping at four (been there done that). There's always management culling available too at cost of daily PH rate. That would be a good option for a youngster. I guarantee you'll see a thousand animals of all sorts. He won't be bored. Just getting there will be an adventure in itself. I just paid the taxidermy bill for eight euros including a big cape buffalo and it was $900 which isn't bad. That bull euro skull only cost $200. We are finishing up a client's huge bull moose euro today at $450 (they are a mega pain - I try to price it so clients go with moose cap mount instead) Still have to pay freight to ship the trophies. Hunting Africa is expensive but not as expensive as you might think.