Thanks, Joe. I have searched both units, and have not found details of the person I am looking for, so I am now of the opinion that he was, in fact, a member of the 4th Texas. This has further been confirmed by another independent source, and also a search of the Texas Confederate Pension application web site, which indicates that he never applied for a pension from that state. The name of the person I am searching for has been indicated, in a New Zealand newspaper, to have settled there after the war, and was living there at the time of the newspaper article in 1910.
A gentleman living near the National Archives in Washington has just indicated that the records of this soldier, in the 4th Texas, show that he was in hospital in Richmond in October of 1862, some two months after the 2nd battle of Manassas, almost certainly confirming that this is the same person who later lived in New Zealand. Thank you for all your help, and it is very much appreciated.