Pretty sure the William Smith in question was the brother of James Smith who married Sarah Holeman's sister, Mary. If so, his parents were Stephen I.K. Smith born 1756 in Orange Co. VA and his mother was Mary (have no other info on her). Stephen died in 1806. His father, Charles Smith, born 1730 in Gloucester Co. VA, outlived his son many years, dying in Surry Co. NC in 1829. He left a will naming all the living children, and grands of the deceased children.
Mary Smith went to TN with many of the children, settling in Overton Co. She's listed on the 1820 census there.
Charles Smith was married to Ann Mallory, born 1737 in Orange or Hanover Co., and died in 1803 in Surry Co. NC.
Charles father was Justephenica Smith, who later changed his named to Stephen I.K.. Ann's parents were John Mallory and Ann (Snell?). Just's parents were Charles Smith and Grace Sawyer~Chas. born about 1680 and Grace in 1684. She was a twin of Margaret Sawyer. She had a brother named Justephenikah Sawyer.