I believe I have this figured out...........Starting off in my opinion the correct unit was Wood's Regiment, Confederate Cavalry (1st Mississippi Cavalry) (Wirt Adams' Regiment)(Confederate). And the roster is online under the category CSA at fold 3.
Seeing Lieutenant Colonel R. C. Wood (Robert C. Wood) as a prisoner with Adams Cavalry is a dead give a way.
However these POW were taken in Lebanon, Tennessee in May of 1862 and not in July of 1863. The unit in 1862 was with Morgan's command but not on the Ohio Raid. Most were taken to Camp Chase and released in August of 1862 per the Dix-Hill Cartel.