According to the score the composers are:

Fred Brooks and Marshall Barer
Copyright 1954 FOLKWAYS MUSIC PUBLISHERS INC N.Y.

I will send the Midi to Alison whom I expect will post to the Mudcat Midi Site fairly quickly. I changed the arrangement a bit, but it's still fairly straight. The Nat Cole version syncopates it somewhat (and improves it in my opinion) but I haven't had the time to play with it too much. It's a great song! Regards, John