Why wouldn't he? Is he not the Head of State for the Vatican, and thus the Commander-in-Chief of their armed forces? Could he not simply order the Swiss Guard to dispose of all their modern weaponry and only maintain their ceremonial weapons and armor?
In the original conception, at least, the Swiss Guards of various European states were mercenaries paid by kings and popes - certainly, had you asked that question five centuries ago, the answer would almost certainly have been 'no'. Moreover, the monarch is the head of state and commander in chief of the British Army, but I'm not convinced that it would disband itself if Charles took the throne and decided that it would be put to better use talking to organic vegetables.