Mr. Sewell, I am in the process of researching this unit and according to information that I have gathered many of the men who were new recruits were unarmed at the time of their enlistment.
Those that were armed likely were armed with guns they had brought from their homes. The arms many have been shot guns, squirrel rifles, pistols, Bowe knives, or even knives fashioned from saw blades.
Some of these soldiers were not issued any arms because the South did not always have sufficent arms to issue to new recruits. The recruits that owned mounts but were unarmed rode at the rear of the formation when they went into battle and obtained the arms from fallen soldiers from both Yankee and Rebel forces. Therefore, there was in all likelyhood a variety of arms used by the men of the units during the entire war.
If you have any info concerning the 13th/16th Battalion please contact me at my private e-mail address, it would be appreciated.