To echo what Doyle said, Sharpshooter battalions in the Confederate Army had nothing to do with sniping or marksmanship other than learning the firing procedures set forth in Hardee's Tactics.

These were battalions organized purely as light infantry, and used as specialists in skirmishing and scouting. Typically, they were armed with P1853 Enfield rifle-muskets, or with the P1856 Enfield or M1841 Harpers Ferry (e.g., "Mississippi") rifles (2-banders). They used iron sights -- not scopes, and otherwise were the same as any other infantry line battalion.

I took part in a living history out at Chickamauga a couple of summers ago where we replicated the 9th Mississippi Sharpshooters in Dyer Field... and it is a rare treat to watch a full battalion deploy in skirmish order, then maneuver and fight under command of the bugle...

Longstreet did have a small detachment of snipers attached to Division headquarters, and Cleburne formed a small detachment (12) of men armed with imported Whitworth rifles in the summer of 1863. Cleburne did have a shoot-off within his Division to determine who would be awarded one of the Whitworths. Sam Watkins describes this in one of the chapters in "Company 'Aytch'" I believe...

Tom