Paul,

As was stated, this is a challenge. Every state that has an 18th anything has at least one S. or William Davis. Some have more than one. Nearly 4,000 W. or William listings.
Try these: All numbers are Microfilm Box , Roll And Number from the National Archives.
U. S., William Davis, Co. B. 1st Al. Cav. pvt. 000263, 0001, 00000576
U. S., William Davis, Co. E, 1st Al. Cav. in Sergeant out Pvt. 000263, 0001, 00000577

The all others are C. S. listings:

W. Davis, Co. A, 1st Al. Cav. pvt. 000374, 0011, 00004449
W. A. Davis, Co. C, 1st Al. Cav. pvt. 000374, 0011, 00004460
William Davis, Co. C, 1st Al. Cav. (misc listed as W. H. Davis) 000374, 0011, 4493

The W. C. Davis I mentioned earlier was in Co. I, 8th Inf. Pvt. 000371, 0011, 00004468

W. N. Davis, Co. F, 18th Al. Inf. Pvt. 000374, 0011, 00004603

If you could get to the National Archives regional office in Atlanta you could spend many hours looking over their compiled service records and possibly, I say possibly, sort it out.

I could have missed some. This was only a quick review.

Wayne Adams