I am no authority on the battle of Wilson's Creek, so I can't really give you a full answer, but one thing is certain: Indian participation at Wilson's Creek was very limited. There are no official reports suggesting otherwise.
I know that a small number of Cherokees from Stand Watie's regiment were there. Watie's regiment was organized at a mass meeting at Old Fort Wayne in the northeastern Cherokee Nation in late July 1861. It appears that Captain John Thompson Mayes (and not Joel Bryan Mayes, as some would have you believe) thereafter led a group of volunteers to join Gen. Ben McCulloch's army advancing into Missouri. This was entirely an "ad hoc" detachment, however, and not a specific company of Watie's regiment, although Mayes was the commander of Company F and Watie no doubt gave the men permission to go. Their main service were as scouts for McCulloch's forces.
Whether soldiers from the Choctaw nation also accompanied McCulloch in similiar fashion, I don't know. But if they did, it was not as part of an established company or regiment. I would suggest contacting Wilson's Creek National Battlefield Park to try and find out more.
Otherwise, the only instance I'm aware of that Choctaw soldiers operated in Missouri was at the Battle of Newtonia in September 1862.