is the site for Texas Counties, and Anderson is first on list.Their list of Confederate Indigent Families of 1863-65 indicates two: (could be same) W. Walker William Walker
This is only mention of a W or Wm Walker, but there is a Geo H. Walker was on pension list and is buried with CSA marker, Pvt Nichol's Company, 1st TX Heavy Art. Regt, buried at Field's Chapel(b. 1839 d. 1922)
There is a book of Texas Indigent Families of CSA soldiers done by Linda Mearse.If you go to your library and ask for an inter-library loan of "The Mearse Transcripts" entitled " Confederate Indigent Families of Texas 1863-1865" you might find further family information.
Also the Historical Society of Anderson County might have information.