I'm going to add my last two cents here, since it seems like Tony is getting advice from lots of well-meaning people, both offline and on.  And I don't want to add to the confusion.  

In looking for the "original" Picayune Butler, I personally would begin by searching digital newspaper sites, concentrating on the period of the 1820s and 1830s.  My favorite newspaper sites are NewspaperArchive.com; GenealogyBank.com; and the British Library digital newspaper site.  My agency and the Library of Congress have co-developed their own beta website for historical newspapers; but I find it hard to use at this point compared with the others.  

After sifting through the early newspapers, I would move on to diaries and memoirs from New Orleans that were either written during the 1820s and 1830s or, like the Robert Buchanan account, refer back to this place and time.  

By the 1840s, everything gets a lot more complicated and a lot murkier.  There are lots of newspaper references to "PIcayune Butler" during this period, but they invariably refer to a popular minstrel song, not to a real person.  However, as you point out, an entertainer in the New York area in the late 1850s was calling himself "Picayune Butler."  I looked at some of the ads for this guy and I'm pretty certain he was a white guy in blackface.    

So I would concentrate on the earlier period,  before the song became popular.  Robert Buchanan (I would find out who he is) in the 1869 Cincinnati newspaper talks about the growing popularity of the word "picayune" in New Orleans early in the century.  He also associates his early banjo player Picayune Butler with flatboatmen.  So these are also leads that I would pursue.    

So that's about it.  If I didn't have my own big newspaper research project (on Japanese entertainers in America in the 1860s and 1870s), I might be tempted to look a little more deeply into Picayune Butler myself.