Good question. I think besides Coppens' 1st Louisiana Zouave Battalion there weren't any other Confederate regiments or battalions entirely outfitted in zouave uniforms. There were, however, many individual companies that did wear some form of a zouave or chasseur style uniform initially, as their early war company uniform or prewar militia uniform. Contrary to popular belief, Co. B, Tiger Rifles, were actually the only zouaves in Wheat's Battalion.
There was the Avegno Zouaves or Governor's Guards, also recruited in New Orleans. According to
Louisianians in the Western Confederacy by Stuart Salling, they consisted of six companies and formed the nucleus of the 13th Louisiana Infantry, so I guess they were essentially a battalion at first. They were mostly of the same cut and cloth, figuratively speaking, as Coppens' and Wheat's Battalions, consisting of many foreign immigrants and ruffian types from cosmopolitan New Orleans. They were said to wear red caps, red trousers and gold braided blue jackets.
I'm not sure if the Avegno Zouaves ever faced off against another zouave unit though; I don't think Salling's book ever mentioned any such occurrence, but not to say it didn't happen. I'll have to look into that. Obviously most of the Union zouave regiments were in the Eastern theater, but I do know the 8th Missouri and 11th Indiana both wore zouave or chasseur style uniforms, at least early in the war, and fought in the Army of the Tennessee.
Like maybe the Battle of Gaines's Mill I just thought of? Because both Duryeé's 5th New York zouaves were there and so were Wheat's Louisiana Tigers but I have no idea if they were ever in direct contact with each other.
Well as for Gaines' Mill, I don't think Wheat's Tigers directly faced the 5th New York Zouaves. IIRC, Taylor's Louisiana Brigade attacked the Federal center at Boatswain's Creek/Swamp. The 5th New York was on the Federal right and faced off against Orr's 1st SC Rifles of Maxcy Gregg's Brigade in a deadly stand up fight; at least that's one of the units they faced.
Also to note, it is believed that by the Seven Days not much of the Tiger Rifle's zouave uniform was left on those guys. Some were just wearing "regular" Confederate uniforms or Louisiana state issue uniforms by that point, maybe with parts of their former zouave uniforms mixed in.