I have searched the records of several "William Singletons" in AL service, one of whom was a surgeon, but, unless he was the surgeon, I don't think any of the others are yours.
I do find a Thomas Bennett Singleton, Pvt., Co. F, 19th MS. Could your man's name have been Thomas Bennett?
What evidence do you have that W.B.S. was a CS soldier?
Thanks! -- Jim Huffman, 43rd MS Infantry