I found a page about the song here: https://www.richardsilverstein.com/2004/01/04/tzena-tzena-an-old-hebrew-chestnut/

The page gives these words for the "wildly awful" translation by Mitchell Parish:

TZENA, TZENA
(translation by Mitchell Parish - 1950 edition)

Tzena, Tzena, Tzena, Tzena
Don’t you know that you’re the darling of the regiment?
Tzena, Tzena, Tzena, Tzena,
All the soldiers want to see you, why don’t you consent?
See the handsome soldiers gaily riding,
Come out from wherever you are hiding,
Won’t you smile a little for the colonel,
Throw some kisses to the rest.
Tzena, Tzena, Bashful little Tzena
Please don’t be afraid of all the soldier boys, for Tzena, Tzena,
All the boys adore you
Calling for you Tzena, Tzena, Tzena

I bought the sheet music published by Mills in 1950, and these are indeed the lyrics Parish wrote. They seem to be close to the original idea of the song, which conjures up visions of the machismo of young soldiers.

As far as I can tell, this is the version that won the copyright lawsuit. This version does not include Hebrew lyrics.