> Maybe MacColl used Trooper to appeal to the US market?

Not likely. He first recorded the song on "Barrack Room Ballads" for Topic, a small English folk label, in 1958.

A "trooper" in the U.S. may be a cavalryman, a state police officer, or a paratrooper. (A local, municipal police officer would never be called a "trooper." Mounted officers are either "mounted police" or "mounted officers." "State trooper" is the usual term for the state police and highway patrol.)