Can't beat Kay Kyser and his "College of Musical Knowledge" band- they were first- before Glenn Miller, the Dorsey's and others- and in my opinion Kay Kyser was the best
Tom Stacks did the vocals on a huge number of tunes for Harry Reser & his Orchestra. His voice on some of those Reser recordings (eg. Here's That Party Now In Person) sounds similar to what we hear here, though not quite as pronounced. No evidence to suggest it was him, and he may have been dead by the time this was recorded.