Another Cartoon Music Question

[Cartoon King]

I am looking for the title to the music featured in a couple of cartoons. It is the song played for the finale to the uncut "September in the Rain" and also used in Tin Pan Alley Cats when the Fats Waller Cat enters the Kit Kat Club. This song is stuck in my head, even though I can't understand most of the lyrics. Anyone know the words, or where I might can find out?

Thanks!
CK

[Larry T]

"Nagasaki"-

but I have no clue as to who wrote it or what other history it has-

Weirdest thing, about 15 years ago I was vacationing pretty far away from home and I went out to a "lounge" bar with some friends of mine. There was a piano player just doing improv of various kinds of songs, and within 15 minutes of my entering the place, he played that very same song- I ran up to the piano and shoved everyone else out of the way and asked him, "Hey- I read the title was supposed to be "the Schelsinger Swing"- wherever did you learn that song???"

He replied, "it's 'Nagasaki' and get away from the piano, unless you're here to style my tip jar with some icing".....