I think the Louisiana Brigade did have a sharpshooter battalion. William J. Seymour, aide to Harry T. Hays, mentions it twice in the memoirs I edited (The Civil War Memoirs of Capt. William J. Seymour). For May 26, 1864, at the North Anna River, Seymour writes the brigade was moved to a hill in front of the railroad and dug in. "Heavy skirmishing in front of our left in which our sharpshooters. [sic] The enemy tried hard to dislodge our sharpshooters . . . but he failed to drive them away. This was one of several occasions during this campaign when our sharpshooters--all picked men--had successfully resisted the charges of lines of battle."
Then in describing the fighting at Fisher's Hill on Sept. 21, 1864: "Towards night the enemy felt of our line in several places by advancing his skirmish line; in front of the position of our Brigade our sharpshooters, deployed as skirmishers, repelled three attacks of the Yankees in line of battle." He goes on to say he was ordered to pick an officer (Capt. Weightman) to relieve the one in command of the sharpshooters, and the man was subsequently killed. "he wished to died on the skirmish line, in the midst of the noble fellows that composed his corps of sharpshooters."
It is possible Seymour is referring to a corps or division level sharpshooter unit, particularly since I never found evidence of a Capt. Weightman serving in the La. Tigers. However, the context in which the citations are used make me think he is referring to the brigade's sharpshooters.