As you might expect, there are hundreds of Smith's. The following which best fits the information you provided was found at Find-A-Grave. The last line states W. J. served in Mississippi. If this is accurate, he was probably not part of Price's Raid. I found Arkansas pension records showing the amounts paid each year to a W. J. Smith of Baxter County up till 1912 when he died and it states his widow is applying for a pension. My search did not find the actual pension which should show William's unit information for either the veteran or widow. If you verify the man below is your ancestor, I will continue to look or maybe some one on this forum with more knowledge can better answer your question.

William J. Smith
BIRTH 22 Sep 1836
Monroe County, Mississippi, USA
DEATH 21 Dec 1912 (aged 76)
BURIAL Custer-Herron Cemetery
Henderson, Baxter County, Arkansas

Marker has a Masonic emblem on it.

1910 Mill, Baxter County, Arkansas
William J Smith 75 (73 age unclear) Miss
Martha Smith 59 Ill

Census shows they have been married 16 years and both have been married 2 times.
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William J. Smith 57
md 17 Oct 1893 Baxter County, AR
Mrs Martha J. Stephens 40
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Buried next to him is his wife Mary J. Smith.
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When the Norfork Dam was being built in the early 1940s this grave was one of many moved from the Herron Cemetery to what is now called the Custer-Herron Cemetery.

Family Members
Spouse
Mary J. Whitehead Smith
1842–1870 (m. 1858)

Children
John T. Smith
1866–1924

Van Dorn Smith
1874–1951

James Knox Smith
1878–1936

Horton V. Smith
1891–1965

Arkansas Confederate pension. W J Smith Co E 4 Mississippi Cavalry, died 12-25-1912
Left by Lindan S. Caldwell on 18 Nov 2014