GUEST,Lighter,

"...Foolstroupe, "Hold Your Hand Out, Naughty Boy" first appeared about 1913. "Fritzie Boy" is a wartime parody..."

I think that you will find that "Fritzie Boy" is a slightly later version of the parody (late war) or possibly an American variant.

The earliest vesion of the parody I've come across was:
"Keep your head down Allyman"
('Allyman' derivd from the French for German 'Allemand')
The rest of the chorus is the same (Jim Dixon's post was the first time I'd seen verses for it).

Regards

W