I am also looking for the sheet music or excerpt from the score. It
appears it may reside in a film industry library in Los Angeles. It
appears that access is restricted to in-person visits and copying
there is cumbersome. On the other hand, if one were to go there the
particular cut we want is fairly short. If I am ever in LA rest
assured that I will visit the library and try to get a copy. But I
have no plans to go there and would not make the trip just to get
the music.

The Peggy Lee recording is probably authentic to the soundtrack as
from my research she sang it in the movie. In the meantime I will
keep searching and if I find it I will email you and hope you will
do the same. My interest is to arrange the tune for TTBB mens
chorus. I heard the song when it was new and it has been in my head
ever since.