Sorry, I'm not up on Napier's Cavalry and would have no idea.
However, here is a twist. There are no Hammonds listed in DeMoss' 10th Cavalry. But, there is a
J. H. Hammer who does not appear previously in Napier's. Could be your Jesse Hezekiah Hammond.
J. H. Hammer, Private, Company D, 10th (DeMoss’) Tennessee Cavalry, enlisted December 5, 1862 at Waverly, Tenn. by Col. Johnson for the war, appointed Ord.[nance?] Sergeant March 19, 1863, paroled at Gainesville, Ala., May 10, 1865
Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Tennessee