rich r's WWI version:
Oh we don't have to hike like the infantry,
Ride like the calvary
Shoot like the artillery
Oh, we don't have to fly over Germany
We're the Q.M.C. [et al]
looks like a re-work on a (Confederate) US Civil War version, parts of which go like this:
If you wanna have a good fight,
Jine the cavalry [3 times]
Rally, boys, around. [3 times]
If you wanna have a good fight,
Jine the cavalry,
Rally boys, around.
Oh, we are the boys who
Rode around MacClellian...
Stuart's people, no doubt.