I'm afraid 'fiddling' goes with the territory, and as you say, could be a problem on the flight. Attention span tends to be short, too, so any activity would only keep him occupied for a short time. A tranquilliser may be the best option.
John has already worked out how to lock his room from the inside, has had the light bulb out (he's tall enough to reach), and goes in and out of other people's rooms, and if the bed is empty, lies down and goes to sleep there.
It's not just puppies that keep us on our toes!