This explains Tandy C. Walker's participation at Wilson's Creek (Oak Hills). Acting on a tip from Tandy C. Walker's bio in "Leaders and Leading Men of the Indian Territory, Choctaw and Chickasaw", by H. F. O’Beirne, vol. 1. page 316, it states "At the opening of the war he joined Col. Carroll’s regiment in Arkansas and fought at Wilson’s Creek and other engagements;", I visited the "Edward G. Gerdes Civil War Home Page" at http://www.couchgenweb.com/civilwar/ and did a search. The search revealed that T.C. Walker, age 22 was a member of Company "B" of Colonel DeRosey Carroll’s regiment, also known as 3rd Regiment (Cavalry), Arkansas State Troops, First Regiment (Cavalry), Arkansas State Troops. This unit participated in the fighting at Wilson's Creek and was disbanded shortly after.
Here is a link to the history and roster of the Sebastian County Cavalry at http://www.couchgenweb.com/civilwar/sebascav.html .
The text of the bio of Tandy C. Walker is at http://www.roark-family.org/Leaders/TCWalker.asp .
Here is a link to an incomplete list of members of the 1st Arkansas Cavalry Regiment, Arkansas State Troops, including casualties from Wilson's Creek, http://www.couchgenweb.com/civilwar/1statecav.html
Hope this helps,
Jim