I don’t think there are any cherries that are resistant to SWD or cherry flies. The insects may prefer a certain species or cultivar over others but none of them are safe. With some early ripening fruits you may be able to escape SWD in your area.
For defense you can bag the fruit, spray Surround, spray an insecticide, or bag the entire tree. Bagging individual fruits isn’t really practical with cherries. Bagging the entire tree can work in arid and dry areas. It doesn’t work in the East because the fine mesh of the tree bag increases the humidity around the tree and makes brown rot worse. You may be able to take this approach in Omaha.