Jeez; I can't leave you guys alone for a minute!
You do the Heimlich maneuver, or whack him between the shoulder blades. AFTER you have determine that he does in fact, have an obstructed airway. If a person can talk, he is NOT obstructed.
The next thing I would do is try to visualize the foreign object and see if I could grab it and pull it out. People frequently choke on large pieces of poorly masticated food. This, BTW is not official Heart Assn. doctrine, but makes sense to me.
Only then would I do a crycothyrotomy. This is where you go through the crycothyroid membrane (the little depression just below your Adam's apple), making a small incision, then putting something like a soda straw or a metal ball point pen bbl. into the incision to keep it open.
This is NOT a tracheostomy. A tracheostomy is done lower down on the trachea, and the presence of the thyroid, which bleeds like stink, in this area mitigates against doing this proceedure in an emergency field situation.
BTW, if they have scalpels in the airplane first aid kit, it is news to me. They don't even have antihistamines, as far as I can recall.
I would use my keychain Buck Titanium slip lock folder for the crycothyrotomy, BTW. I do carry a Parker T-ball Jotter in Stainless Steel just so I would have something to poke down the guy's incision also. Well, actually I more commonly use it to write checks, but it is always there.
Walter Welch MD, Diplomate, American Board of Emergency Medicine. yada yada yada