In Wheat's 1st Louisiana Special Battalion (aka Louisiana Tigers), Company B "Tiger Rifles" and Company D "Catahoula Guerrillas" of the battalion were both armed with M1841 Mississippi Rifles, at least initially. The other companies of the battalion were issued M1842 and M1816 smoothbore muskets.
That's what Wheat's Tigers carried into battle at First Manassas, however that was before they became part of the 1st La. Brigade. When they were in the brigade during the Shenandoah Valley Campaign and the Seven Days they were likely also carrying a mix of different arms picked up off the field at Manassas and later at Front Royal, Winchester and Port Republic.
And that's according The 1st Louisiana Special Battalion by Gary Schreckengost. I've yet to find anything concerning the weaponry of the other units in either brigade, however.