You had said you suspected Charles Herron might have been killed in the war. Consequently, what I searched were the war dead listed in the Archives and the American Battle Monuments Commission database of those interred overseas. Both of these resources are searchable online.
I have also searched these databases for a Walter or Thomas Herron. None is listed in the ABMC records. No Thomas is listed in the Archives' New York or South Carolina Navy casualties. There is a Walter Lee Herron from New York listed as killed, but his father's name was Ellis Grant Herron. Without the state AND county, the Army records are very difficult to search, so I can't be sure there.
As for any records that might exist in the event that they were not killed in the war, one would have to pursue that through other avenues.