Not being an expert here, but from what I understand the Ivestarms (Cabelas), Thompson/Center, CVA or any other "Hawkens" would not be appropriate for Civil War Reenactments using military weaponry.
Here is a good listing of Civil War Era weapons:
http://www.n-ssa.org/
http://www.edsmart.com/jz/guns.htm#usrifles

Bascically you either want NSSA (North South Skirmish Association) approved or some civilian weapon that is appropriate to the era.

The Lyman Great Plains might be a better alternative for a Civil War Era "Civilian" weapon.
www.lymanproducts.com

Also: www.dixiegun.com Look for NSSA weapons.

Or, a Southern Mountain Rifle style for Civilian.

Also, check these out.

http://www.donstith.com/muzzle_loading_rifles.html

Good luck!

Tahquamenon