The locks seem to be an arguable topic in this thread. Here's from the TSA's website...

- The container must be locked. A locked container is defined as one that completely secures the firearm from being accessed. Cases that can be pulled open with little effort cannot be brought aboard the aircraft. Federal regulations prohibit unlocked gun cases (or cases with broken locks) on aircraft.

- TSA inspects all firearm cases at the ticket counter. Travelers should remain in the area designated by the aircraft operator or TSA representative to take the key back after the container is cleared for transportation. If travelers are not present and the security officer must open the container, TSA or the airline will make a reasonable attempt to contact the owner. If contact is not made, the container will not be placed on the aircraft.

So you should absolutely use non TSA locks and carry the key with you. You and only you should have access to it. If TSA wants to see inside they need to find you and have you there when they open it.