I have traced my family in OK back to one Walter Adair who came to OK on the Trail of Tears, year unknown.This is not one of the well known Walter Adairs (Black Watt, Red Watt) as far as I can tell, as an interview with his grandson (Isaac Batt, b. 1867 in Delaware Cty OK) describes him as a subsistance farmer in the Cowskin Prairie.
He had at least one son, John (b. 1849 in Delaware County OK, married Mary Hawktawter, b. 1851), whose last name was Batt -- I read that Batt was the Cherokee way of saying Adair, is that true?
Based on the interview with Isaac, it is possible that Walter Adair's wife died young, as he has no recollections of her.