The 3rd Georgia Sharpshooter Battalion organized in early May 1863 when General Wofford detailed fifty men from each of the five commands in his brigade. Officers and men were already enlisted in Confederate service and serving in Wofford's Brigade. George Smith of Co. "A", 3rd Georgia S.S. Battn., transferred from Co. "B", 18th Georgia Regiment, the "Newton Rifles." You've seen a summary of his capture and imprisonment. This man didn't use a middle initial and his age isn't listed, so you're still not sure about him.
What about other men named George T. Smith, the name you really want? A man named George T. Smith enlisted in Co. "H", 28th Georgia Regiment. As shown on the 1860 census, he's from Washington County GA.
Only one other man by this name is indexed for a Georgia unit. He belongs to another company from Newton County, Co. "A", Cobb's Georgia Legion. It just so happens that this command also served in Wofford's Brigade, and this soldier was also captured near Farmville VA, Apr. 6, 1865. Interesting coincidence. Age isn't listed, but I believe he's the man you want.
Copies of his military service file are available here --