So the lock on the bag can be a TSA lock. The pistol case should not be one of the locks that are TSA mastered. You can buy the master keys btw. I'd an airport gives you grief make sure you have a printed copy of the regs right with your pistol case. I think Atlanta had some issues where they just cut locks when a firearm is involved though they should not be.
That's why I use TSA approved locks.