Hi, Lea. Sounds like you have a very nice set. From your description, I don't think that I would refinish. The scratches can be minimized and to a lesser extent, so can the loss of color. Since the sun has taken the color away from either the wood or in the finish, it is impossible to replace it. However, I think that it can be minimized. Cherry does tend to darken over time and perhaps some of the color will come back when it is out of the sun.
I would try any of the following; Watco Danish Oil Finish, Deft Danish Oil Finish (Deftoil), Minwax Tung Oil Finish, but my choice would be Minwax Antique Oil Finish. Follow the label directions.