Thanks to a post on this board I knew to go to Harbor Freight to purchase new blades for my cutters.
While changing the blades figured there has to be a safe way to handle them. I used a magnet attached to a short plastic handle that is used to pick up canning lids out of hot water. It was easy to handle those blades with care.
Then I taped the used blades to the inside of a large styro plate, and taped another plate on top before putting into the trash. I wouldn't want the trashman to become a victim of a wayward sharp edge.