The actual song is "Bag of Rags" written by W.R. McKanlass in the early 1900s. The particular recording they used on TPIR was retitled "Keystone Kapers" and is on a Spike Jones album called "Rides, Rapes and Rescues." The Race Game track is on the same album.
Considering its copyright status, there are a million recordings of it out there. (Though if you want the specific one they used on TPIR, I can hook you up with an MP3.)