Cannot help with the name of the song, but it does sound like Satchmo (not sachimo) - Louis Armstrong, doing some scat singing.
After the initial opening the first "solo" is on the clarinet and it does sound a bit like Benny Goodman.
Benny Goodman did tour with Louis Armstrong in the early 1950s so dont know if it is a recording from that event.
It does sound like it is perhaps a live concert, even though I cannot hear an audience, it just seems to have a feel of a live concert.
There also does seem to be a number of solos one after the other like are featured in a live concert.
I have searched the web for an album by Goodman and Armstrong but cannot find one (does not mean there isn't one, I just cannot find one - Goodman and Armstrong both produced hundreds of tracks in their lifetime).