Yep, that's a "Chüermutz" - some more info here if you haven't already found it:
https://www.trachtenvereinigung-bern.ch/trachten/maennertrachten/mutz
As these are traditional garments and the styles don't change, it will be really hard to put a date on this... Possibly the materials and the way it was made hold clues. I can see some of the seamstresses mentioned on the at website offer evaluation services against a fee, which might include dating, but they will probably only do that in person.