Bryan's Battalion, which ultimately was the core of the the 2nd Cherokee Mtd Volunteers (Adair's), as well as the 1st Cherokee Mtd Volunteers (Watie's) included some citizens of Missouri and Arkansas and non-Cherokee who lived in the Cherokee Nation.
Early in the war, Watie and Bryan operated in the northern Cherokee Nation, northwest Arkansas, and southwest Missouri. The Indian units could not be required to leave their own nations without their consent so whites in the Indian units knew they would be operating close to home.
As you mentioned, there is a James Wigginton in Watie's 1st Cherokee Mtd Rifles who was enrolled at Ft Davis (north side of present Muskogee, OK) and wounded near Ft Gibson (just east across the Arkansas River from Muskogee).
Where were your Wiggintons and what were their ages on the 1860 Census?