Given that the fedora wasn’t invented until the late 19th century, it is really difficult to argue that it is halachically required.
And if people knew the origin of the hat and how it was named, it would NEVER be worn by frum Jews! It was first used as part of a costume for the notorious licentious Jewish apostate actress Sarah Bernhardt; “Fedora” was the name of her character. For decades the style was only a women’s hat and men only started wearing the style in the 20th century around the time of Bernhardt’s death.