If O.A. Williams was conscripted as thought, he might have gone along with a group with or without his consent.

Morgan Co., MO, had no Confederate recruiting station but the guys went to adjoining counties or to Gen. Price along the MO River.
Some Morgan Co., MO, residents who went to the Confederacy were never credited or listed as from Morgan Co. We think there wee 100-200 men from Morgan Co. who served in the Confederacy. (600-800 Union)

Since his father also went to be with him, despite being 52 yrs. of age, you might ck. out the father's information: Daniel Williams (blacksmith) born. in Auburn Co., NY, emigrated to Morgan Co, MO 1837, from Ohio. His wife was Mary McLaughlin from Richland Co., PN. He was 52 yrs.of age at the 1860 census, Mary was 44. You might look at the surrounding counties: Camden Co., Cole Co., Cooper Co., Boone Co., Benton Co, the Sedalia area, or Moniteau Co. had some.There weren't many Confederates in Miller Co.

Daniel was imprisoned by the Union army and released when he was expected to die. There may be prison records or even hospital records.

Hope you find what you are looking for. I have a few inquires out and we will see if anything turns up.