I have a photocopy of the music of Joseph John Davilla's "The Mysterious Axman’s Jazz (Don’t Scare Me Papa).” [The comic cover has been reproduced in several books.] Moreover, I have undertaken exhaustive research on the New Orleans Axman serial murders to which the song refers. If you would like to contact me privately with your questions, you can email me thru IMSLP.
I don't know whether the New Orleans Historical Society's copy is a published print or a photocopy, like mine. I am aware of only one extant original of this song -- and it's not one held by the NOHS. That is not to say the NOHS does not have an original. I do not know what they have.