In General Hindman's copybook of telegraphs there is some cryptic reference to the need for improvised arms to arm the new recruits. As you know Company C, 26th Arkansas were some of the earliest of these recruits. Hindman also ordered all Gunsmiths to be sent to Little Rock for that purpose to convert civilian arms like squirrel rifles and Shotguns which had been collected to military use.
Off course we have a time lineline problem as to when the 26th Arkansas was in Pine Bluff and Hindman arrived in Little Rock. I would wager a guess that this weapon would be one of those early conversions which had been made by a gunsmith in Pine Bluff. The 1860 census in Jefferson county can sometimes be difficult to read. You would be the expert on this but wasn't a few companies ordered to DeVal's Bluff. And if so wouldn't they have been armed with these types of weapons?
Weapons procurement seems to have been a major problem until late July and August 1862, with the arrival of proper military grade weapons from the east by Parson Missouri Brigade and from Vicksburg.