If we didn't have all the unconstitutional restrictions on carrying in public places, pilots could merely carry their weapon in their chart case, just like they probably did before the anal retentive gun grabbers got into the act. As for "extensive" training, I fail to see why any more training should be required for airline pilots than for concealed carry permit applicants in most states. Say 8-10 hour of combined classroom and range training and qualificatioin. They aren't going to be making any long distance pistol shots inside the cockpit, so making use of the original point and click (hopefully point and bang) interface shouldn't require much training. These are pilots after all, who have to meet moderately stringent physicial requirements just to begin their training, or maintain their rating. I don't think shooting some Jihadi at 3 or 4 feet should be a big technical or physical challenge. The "when to shoot" part would of course be covered in the classroom portion.
What makes this insistence on "extensive training" so ridiculous is the fact of the 15 minutes of weapons and bomb identification training handed out to the screeners when they were federalized.
The pilots are responsible for the safety of the aircraft, crew, and passengers. Allow them the tools to do the job. That would include a reasonable amount of training, but nothing more than the equivalent of 1 working day.