Why is Mrs. Stout a man?

I think it's because a guy in drag can make a very unnattractive lady.

During the silent films, if they had a female character that would have to do stunts, it wasn't uncommon for a man to take on the part dressed in drag. Charlie Chaplin was in drag in A Busy Day, and at the end of the film his character is thrown off of a pier, apparently some filmmakers deemed these sorts of stunts too dangerous for a woman, so a man in drag was cast.

Maybe this was the reason for this casting as well, as some of the skating falls could be pretty hard on the body.