Why would you want to? Save the farewells for those worthy of the effort. Any arrogant or egotistical person won't really appreciate it anyway. If he is your employee, as in: he works for you, be very careful what you do, you don't want to seem as if you are rewarding his attitude in front of other employees. I would recommend something as minimal as possible and only dictated by custom. A firm handshake and a nod is about all I personally could manage for someone like that.
I would just be classy about it and get them out the door. One more day is not going to hurt anybody. Do whatever you have done when others of the same or close to the same position and tenure have left. It will be over before you know it!