I searched Ancestry for James Ware and I have a few possibilities. James B Ware is in 2nd georgia cav state troops. James H. Ware was in 35th georgia infantry. James m. Ware was in the 21st Georgia. The James M. Ware in the 21st Georgia is the most likely to be your guy since the 21st Georgia had companies from ROme and other northern Georgia counties, but I don't know if Catoosa had a company in the 21st.

I know that men from Catoosa joined the 1st Confederate georgia, and I think the 9th or 11th Georgia, and those units did not have a James Ware in them. Better help is on the way like George Martin or Alan Pitts. I just wanted to let you know what i found.
Take care!!
JAck