I think non jews (unless they are little kids, or adults who think like little kids) understand that Chanukah is a jewish holiday. Of course one should use seichel. If you walk in and announce we are here to visit the sick and bring a little happiness, then yes, include the non jew.
One of my children was hospitalized in NYU Medical Ctr a number of years ago. The ladies from the various bikur cholims always offered a danish or other treat to the non jewish child (and his parents and visitors) whenever they came, which was several times a day with the myriad of wonderful bikur cholims and their volunteers that came through the hospital every day. The Roman Catholic father actually told me he had a new found respect for “hasidics” after seeing their selfless chessed for almost a week, and how they extended it even to a non jew, graciously, with a smile.