Cool. I didn't agree with some of his policies and decisions, but in my brief meeting with him he was very personable and seemed absolutely unimpressed with himself. He is absolutely adored by the Secret Service people on his detail. I can easily see him doing something like that.
It probably belonged to the Navy, but could have been a personal weapon. My understanding is back then it was not uncomon for an officer to keep their issue weapon (handgun) even after leaving the service.
It most likely listed as battle loss. The military didn't use to be so anal about guns.