On Cajun Fais Do-Do, from arhoolie, Adam and Cyp recorded "la Cherokee", but I think it was recorded around 65. I would think the 1st post-war version would've been earlier than that though.
The one from Arhoolie was a field recording that Chris Strachwitz did. I guess it sounds right, I've just never thought about when the recordings were done.
This may not be too helpful, but I did find some interesting information about Cherokee Waltz,
First, there is a version of Cherokee waltz on the ACE label CDCHD 353. The CD is a Shirley Bergeron compilation. This version was recorded at Marc Savoy's Music Store in Eunice in late 1969. It was originally released on Lanor 569 (I think it was a 45) and later released on Lanor LP 1001. Shirley Bergeron, Alphee Bergeron, Noah Bourque and Marc Savoy play.
Second, there is an interesting version On An LP titled "La La Louisiana Black French Music," The label is Maison De Soul. The artists are Eraste and Bebe Carrier. The LP was released in 1977. This version was recorded by Nick Spitzer in 1976.
Third, on Folkways FA 2620, titled "Cajun Home Music," there is a version of Cherokee Waltz by Cyprien Landreneau and Delia Landreneau. It was recorded by Gerard Dole on September 4th 1975 in Mamou. Unfortunately, I do not have the descriptive notes that came with the LP.