Thanks, John. Probably it's not an Oklahoma dance at all. The FOLK DANCE FEDERATION OF CALIFORNIA page linked to above says:

This dance was taught by Rev. Larry Eisenberg at the Pacific Recreation Laboratory School, Asilomar. California, September 1947. This progressive type dance is popular in the Southwest, particularly Texas. The title "Oklahoma Mixer" is used here because the present version was learned in Norman, Oklahoma.

MUSIC:
Record: Folkraft 1035 "Rustic Schottische"; Columbia 37332 "Starlight Schottische"; Coral 60792 "Shepherd"s Schottische"; Coral 965517"Rustic Schottische"; MacGregor 400, MacGregor 5003 and National 4535 "Schottische", Folkart LP-105 "Fiddler's Schottische".