Is it permissible to wear a face mask on Shabbos in a place with no Eruv?

One may wear a face mask in a reshus harabaim (public domain) on Shabbos if the face mask is protecting the person. This means that if one is wearing a face mask properly in a way that it covers the nose and mouth, one can wear it outside. However, if the face mask is merely being worn on the chin or hanging from one ear, the face mask is not protecting the person and serves no function, therefore one would not be allowed to go outside with it in a place with no eruv.