Walrus, you may well be right. The "Fritzie Boy" version was sung by Americans in 1918.

The next verse went something like,

Keep your shades down, Mary Ann !
Keep your shades down, Mary Ann !
Late last night,
In the pale moonlight,
We saw you!
We saw you!
You were standing by the chair,
Taking off your underwear.
If you want to keep your secrets from your future man,
Keep your shades down, Mary Ann!