I have two questions. First, what evidence do you have that this man was in Confederate service? Second, what connection does this man have to Texas?

A man named Azariah Graves Walters lived in Pittsylvania County VA, born Mar. 18, 1810, and died Sept. 22, 1899. He married Martha Mary Carter Oct. 24, 1845.

This article states that the title 'captain' may be strictly honorary --
http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=caswellcounty&id=I13308

Walters was a wealthy widower who operated a mill. I can think of no reason for him to have enlisted in the military during the war.