Nope, its not a Stetson. Looks like JC Penney/Marathon had the first Whippet hat. Ads are from Oct/Nov 1927. Interesting that the dimensions of the hat in the sketches could easily be a hat from the mid to late 1940's. Just for the record, Stetson Shoe company did have a Whippet model shoe in 1925...
B
B