As it happens, I went through the same experience. I listened to a couple of recordings of the tune and tried to make a lead sheet by ear. Here's the lead sheet to Black Cat on the Fence that I came up with for inclusion in my mini Filofax. It's actually in Bb but I put it in C to suit my transposing cornet.
My friend Brian Hutchinson in Australia has much more recently sent me a link to the American Music recording made in 1949 by Louis Delisle's Band in a private house in New Orleans. Here is a picture of the band that Brian sent to me:
The musicians are (left to right) Johnny St. Cyr, 'Big Eye' Louis Nelson Delisle, the tune's composer Charlie Love, Louis Nelson, and Ernest Rogers. Missing from the photo is the string bass player Austin Young.
And here is a link to the recording:
I had never been sure who wrote the tune, or when. The record tells us it was Charlie Love. (Recently a source gave the composers as Waller, Brooks and Razaf in 1929. But I suspect that is wrong: I think this source was confusing it with Black and Blue. So I'll stick with Charlie Love.)
Ken Colyer made Black Cat on the Fence popular in England a few decades ago. Listen to him playing the tune: