About 35 years ago an older friend told me he used to sing part of this at the University of Chicago in the late '40s.

As I remember it:

You can do it if you wanna,
But you better do it right.
And you better not do it
Like you did the other night.
'Cause if you do,
I'm telling you,
You're never gonna do it again.
(I mean take my picture!)
You're never going to do it again!

But he just recited it to me without a tune.

He believed this was the whole song.

William Wallrich (a WW2 veteran), "Air Force Airs" (1957) has this. His book includes no tunes:

                "THE COED AND THE CADET

An old one - popular in World War II and Korea.

The coed and the cadet were courting, I declare,
Down by the gate; they didn't know that I was there.
Oh, the coed she was bashful and the cadet he was shy,
He asked if he could, and this was her reply:

'You can do it if ya wanna,
But you'd better do it right,
And you'd better not do it
Like you did the other night!
'Cause if you do, I'm telling you,
I'll never let you do it again -
I really mean it -
I'll never let you kiss me again.'"