Technically, I don't think it is allowed, but nobody is going to question a General on something like that.
I remember back in the 80's when we went into Grenada, there was at least one enlisted man who had his personal handgun (a revolver) in his ruck sack when he jumped in. When one of the other men that jumped into the southern airfield ended up with a bent barrel on his rifle as a result of the jump, one of the other members of his platoon handed him a revolver to use until he could "pick up" something else.
Back then, something like that never got questioned unless something went wrong, in which case, you were just SOL.