The W. J. Smith in the 27th Ark who enlisted in Fulton County was 22 years old in Feb 1863 (born about 1842) and born in Tennessee.

The W. J. Smith of Henderson, Baxter County applied for a pension (#3027) in Aug 1904. On his application he states he was in Company E, 4th Miss Cavalry. His proof of service was the sworn statements of two comrades, J. A. Williams and G. W. Ward before a notary in Lee County, Mississippi. Both swore W. J. Smith enlisted in May of 1862 and served to July of 1865. The pension was approved and W. J. was awarded $50 per year. There are pension records showing how much he received each year until 1912 when he died. Other than name and county, these records do not provide any other information as to service. His widow then applied for the pension.

Based on service records for the 4th Ms Cav, Pvt. Williams was captured in Jan 12, 1864 near Port Hudson and paroled with 120 other privates on August 22, 1864. There is only one company muster showing Mar to June 1864. He was present, but on special duty as a head quarter's courier. This record conflicts with his capture and parole, but possibly whoever filled out the muster did not know he had been captured. He was under Gen Taylor's command when surrendered in Alabama in May 1865 and paroled.

Other than census and marriage records in Ancestry, this is all I can find for W. J. Smith of Baxter/Fulton County, Ark. There were multiple W. J. Smiths in Ark and Miss. You will have to decide which record to believe.