Your 1863 Sharps carbine is a significant piece of American history. With the arsenal inspectors stamp on it and near certainty of it having been used in the War Of Northern Aggression (as the Southerners called it) it has quite a bit of value. Don't let the lack of finish fool you, antique guns are judged differently than modern firearms are, and yours is in very good to excellent condition.
Don't let someone talk you out of it for less than 5-6K. That's right, it's worth that much. If it was mine I would keep it and cherish the memory of the relative or friend that thought enough of you to leave such a special piece of history.