I have heard back from the Williams Research Center,The Historic New Orleans Collection about this item

The Historic New Orleans Collection

but it was not the answer that I wanted to hear. They told me the following:

"We have processed your research request and have located the sheet music for J.J. Davilla's "The Mysterious Azman's Jazz (Don't Scare Me Papa) in our collections. Unfortunately, the sheet music does not include lyrics to the song. On the bottom of the second page, however, the phrase "Lyrics reserved for special mechanical reproduction" is included, therefore it seems likely that the song does include lyrics that we currently do not posess."

Can any of you sheet music collectors tell me if that phrase "Lyrics reserved for special mechanical reproduction" was a usual phrase on sheet music from that time?

So the search for the lyrics (if there are any) continues for the moment.