Lucy --
Thanks for your inquiry. The "Wilkinson Minutemen" was a local defense organization rather than a Confederate military unit. Companies "A" and "B" organized in October of 1862.
Minutemen were expected to be prepared to leave home at a moment's notice to take care of a local emergency. Obviously this wasn't possible if a member wasn't at home. Some of these minutemen later joined Confederate units, but not this man.
I find no record of anyone named W. C. McLean in a Confederate military command. Perhaps another family member who served in the Confederate military was a casualty in the Chattanooga Campaign, or perhaps W. C. McLean died during a visit to Chattanooga after the war.
What else do you know about this man? Perhaps his occupation or physical condition kept him out of active service.