"On Sunday I walk out with a soldier" was in "Oh What a Lovely War" too - I've got a feeling that might be Boer War vintage.

This site - SOLDIERS' SONGS: THE FOLKLORE OF THE POWERLESS is well worth looking at - and it's got a different set of words to "I don't want to join the army", claimed to date from the Peninsula War against Napoleon:

I don't want the Sergeant's shilling,
I don't want to be shot down;
I'm really much more willing
To make myself a killing,
Living off the pickings of the Ladies of the Town;
Don't want a bullet up my bumhole,
Don't want my cobblers minced with ball;
For if I have to lose 'em
Then let it be with Susan
Or Meg or Peg or any whore at all.

(There's a second verse as well, which would constitute bawdy drift of this thread.)