Can you not make him a service dog and take him on the plane with you?
google making your dog a service dog. It is as simple as sending a 50 dollar check in and getting the packet in the mail.
Then you can basically take your dog anywhere as long as you have a disability.
My disability would be getting nervous in crowds or something.
PLEASE DON'T DO THIS!!!! Because so many people ARE, and because the dogs running around with those fake certificates are NOT performing in any way like true service dogs, there is legislation in the works that is going to make it increasingly difficult and expensive for folks who really DO need service dogs, to get them. And then they will face a lot of hassles that right now they are protected against thru ADA.
You should also know as a sportsman, that YOUR dog is protected against certain legislation here in Texas, thanks to the Lonestar Working Dog Association. (Google Working Dog Preservation Bill that we worked with Rep. James White to have authored, sponsored and passed - built into the Senfronia Thompson's "Puppy Mill Bill.")
That same legislation protects police dogs, service dogs, herding dogs, hunting dogs and SAR dogs... any "working dog." When we give reasons to cry foul, we shoot ourselves in the foot and stand to lose these protections.
I am pretty stringent in the dogs I get certified, and like a lot of people who train and use real service dogs, we cringe when we see "puppy foo-foo" running around with fake 'credentials.' They are a true threat to the protections REAL service dogs have earned - and deserve. That's a high price for others (who NEED service dogs) to pay on account of those who abuse this loophole for convenience or selfishness.