What Military branch least likely to go to war?

The merchant marine is not part of the military, the term refers to a commercial industry, I assume that people who think merchant mariners are in the military also think Alaska Airlines i part of the Air Force.

Now to answer your question, it depends on how you define combat, many in the USN are in combat, yet never hear shot fired, same with the USAF, for that matter there are many in the Army or Marines who, while technically in combat are never really near the "front" (though in most modern wars the "front" wasn't real specific)

A cook on a navy destroyer is more likely to be in combat than an instructor in the Army