Ken,
I've looked a bit into this question before, but as you know, I'll have to rely on memory where I am right now...
Anyway, Watie's regiment (or battalion initially) had just begun the process of organization towards the end of July 1861 at Old Fort Wayne. That was only a few miles away from N. Bart Pearce's Arkansas State Troops camp across the state line. A number of men who would soon afterwards serve in Watie's 1st Cherokee Regiment were actually in service with various units of Pearce's brigade, which was discharged within weeks after Wilson's Creek. This included Elias Boudinot, who was a private in a cavalry company from Fayetteville, Arkansas (the name of which I can't recall right now, but you'll find it on the Edward Gerdes Arkansas in the Civil War site). My theory is that there was communication between the camps of Watie and Pearce in the days before Pearce started off towards Missouri, and that some of Watie's men rode off with Pearce's cavalry to Wilson's Creek. This probably happened with Watie's approval, but their numbers must have been quite small, since no Confederate reports explicitly mentions a detachment from the 1st Cherokee regiment participating in the Wilson's Creek campaign. Thomas Anderson, Watie's Swedish adjutant, mentions such an ad-hoc group of volunteers from the 1st Cherokee regiment who were at Wilson's Creek in his (rather fanciful) article "The Indian Territory 1861-1865", published in the Confederate Veteran in 1896. I seem to recall that I found a couple of other references as well, but I'm unable to cite them now. But Stand Watie himself or the 1st Cherokee Regiment were definitely not at Wilson's Creek, although some of his men were present, but then as members of and/or temporarily attached to Pearce's Arkansas brigade.