Ken, I've never seen anything which specifically describes the route Dawson's 19th Arkansas Regiment took on the return trip to Arkansas, other than an indication that, unlike their march to Fort McCulloch, which was via Fort Smith, the march from Fort McCulloch was direct to Center Point, Arkansas.

Here's a brief description of their march TO Fort McCulloch -- Leaving Arkansas near Ft. Smith, they followed the Texas Trail through Indian Territory, which extended southwest from Ft. Smith to the vicinity of Dennison, Texas. The trail crossed Middle Boggy Creek near present day Atoka, Oklahoma, passed Boggy Depot, and on through the Oak Forests to Nail’s Crossing on Blue River.