The first Skeet Gun to appear in a Remington Arms Co., Inc. catalog is the Model 32 Skeet Gun in the March 1, 1934, catalog --
Model 32 Skeet Gun, March 1, 1934 catalog.jpeg
By the February 15, 1935, catalog the Model 31 Skeet Gun --
Model 31 Skeet Gun, Feb. 15, 1935 catalog.jpg
and the "Sportsman" Skeet Gun --
Sportsman Skeet Gun, Feb. 15, 1935 catalog.jpg
were added to the offerings. And the conventional wisdom seems to be that they introduced their Parker Skeet Gun in 1934 as well.
So, it seems that our U.S. manufacturers were actually getting on the Skeet bandwagon in the 1931 to 35 time frame.