Here's an old recording by the popular ragtime artist Billy Murray:

http://ia311509.us.archive.org/1/items/BillyMurray_part4/BillyMurray-TheyGoWildSimplyWildOverMe.mp3

This next one is a link to the Leake Co. Revelers' record I have. I found it on Honking Duck

http://honkingduck.com/78s/listen.php?s=20151A

It was recorded by two more country groups in the mid '30s: The New Dixie Demons and (as "They Go Wild Over Me") The Tune Wranglers.

Source:Country Music Records   A Discography, 1921-1942 by Tony Russell

(Which also lists LCR and HH-S versions.)