Now, you know this is a bawdy song in its home grounds - the army.  Not just "off color" or suggestive.

A. From Legman/Randolph, an example typical of of verses improvised by soldiers on the march.  It's collected in Arkansas in 1953.  He says it was the most popular song for both British & American troops in WW I.  I'd note that this is a "dynamic" song - it's nature includes the creative spontaneity as well as known standard verses.

            Oh, the French they are a funny race,
                    Parlay-voo?
             The French they are a funny race,
                    Parlay-voo?
             The French they are a funny race,
             They fight with their feet
             And fuck with their face ---
                    Hinky-dinky, parlay-voo?!

(He points out these French marital and martial arts (cunnininctus & savate) were both quite unfamiliar to most Yankee doughboys.  I think this upgrades the song in cleverness beyond the usual.)
 

B.  From a 1929 set version learned by children from returning soldiers.  (Compare with Silverman, above.)

            The First Division went over the top,
                    Parlay-voo?
            The Second Division went over the top,
                    Parlay-voo?
            The Third Division went over the top,
            To circumsize the Kaiser's cock --
                    Hinky-dinky, parlay-voo?!

       From two 11-year-old girls from the northwest coast, 1929 - what he calls a classic version:

            Mademoiselle from Armenteers, (3 times)
            She hasn't been fucked for forty years,

            She was true to me and true to you, (3)
            And true to the whole damn Army too.

            The first three months and all was well,
            The second three months she began to swell,
            The third three months and she gave a grunt
            And a little Marine jumped out of her cunt!

He refers to and agrees wit the comments in Brophy above but calls the text "sadly expurgated."  Gordon's Inferno collection has some good verses, too.  I'll have a look there tomorrow.