Despite this fact, I saw a movie in which Laurel and Hardy became soldiers!
Was it Beau Hunks or The Flying Deuces,in which case they would have been in the French Foreign Legion?
Or perhaps Pack Up Your Troubles where they were part of the AEF fighting in the trenches of France in World War I?
There there is Bonnie Scotland where they end up in a Scottish regiment in India.
And lets not forget the 1941 film Great Guns even if it wasn't made in the 1930s.
It was definitely the American army of some sort, so must've been
Pack Up Your Troubles or
Great Guns. I don't remember it in detail, but I'm impressed by your knowledge of this wonderful duo.