I read with interest the posts on William Washington Cavender. I think from reading the posts and some information I may have just found about the image your referred to (is this a young man holding a pistol towards the viewer? wearing a kepi with sockcap?)
The information that I have is that William was the son of Obediah Cavender, a farmer in Coweta County - he did serve in the 7th but enlisted in the 1st Georgia Cavalry (1860 census in Newnan) on May 1, 1862 in Cartersville in Co. K, he lived in the community of Rio, Coweta Co.
If in fact this is the man's image, then this would not be your ancestor as you described a different father.
Also the last person that posted indicated there was a WW Cavender buried in Coweta County.
Best wishes, Dave