One more possible fit:
Sgt. George J. Smith, a 25 year-old Farmer. Enlisted on 5/14/1861 at Hampton, VA into "B" Co. VA 3rd Cavalry. He was listed as wounded 5/15/1864 (place not stated) (Estimated day. Gunshot wound to the head) He died of wounds on 6/17/1864 at Richmond, VA.
I did a search for a C. or C. H. Smith in Virginia CSA units, no joy.