With a tux? I'd suggest a Rohrbaugh.
Less formally dressed? If I were Q (and if him being an American meant an American gun), I'd perhaps supply him a forged stainless steel 1911, commander length, with a Melonite / Tennifer finish and Crimson Trace grips. Threaded for silencer, and naturally it would also fire grenades. [EDIT: that is to say, it would launch small grenades with a special adapter and appropriate booster cartridges -- I am not asking for a tiny-bullets-that-make-huge-explosions special dispensation.]
In a movie (AND ONLY IN A MOVIE!), it would be a "smart gun" -- Q would give vague but urgent warnings that James must never allow anyone else to shoot the gun; when at some point a bad guy does so, thinking how rich it would be to shoot Bond with his own gun, that plan backfires, and the gun either explodes with a giant KABOOM, or jabs the bad guy with a dose of something which either kills him or makes him instantly groggy. To this, James should look quizzically taken aback.
timothy