Yes, Cunningham's book must certainly be read with caution. It is not very well researched compared to later works, and based on what seems to be a great deal of secondary sources. When it comes to the war in Indian Territory, sources are comparatively scarce, so myths like the one re. 1000 Cherokees and Choctaws at Wilson's Creek have a tendency to reappear endlessly in other hastily researched works. Another example is the Indian participation at Pea Ridge, which is often stated to be from all regiments of the Five Nations. It was Van Dorn's wish to have all of Pike's Indian regiments there, but in fact only Watie's and Drew's Cherokee regiments made it to the battlefield. Another classic myth is that all Indian units were hopelessly unreliable and deserted en masse - which of course Drew's regiment did, but you will find general statements of this kind in otherwise scholarly works.
As regards well-researched books on the war in Indian Territory, Wilfred Knight's "Red Fox" and W. C. Gaines' "The Confederate Cherokees" are generally very reliable (though not entirely free of mistakes).