I found more mentions of the music hall song, which was on the go from about 1918-1920's and was certainly being sung around, and would have been out in sheet music - but as I say, it may not be the one you are looking for, and isn't Irish.

. The Worse You Are the More the Ladies Like You is an atrocious thing to sing to children. It's the bad lads that get the nice girls declares the ballad writer. Mr. Collins should cut this out at once. ..   Sunday Mirror December 1919.