Perhaps you can buy a second set of cup holders that are slightly bigger than the ones that will hold the actual cup... then you could use some sort of refreezable icee bags (the blue jelly type) and then sandwitch that in between the two cup holders..keep the bottom cup holder set into the table and then only have to be able to remove the top cup holder to refresh the icee jell bag?
just a thought...
ohh the bottom cup doesnt have to be stainless steel, but maybe some type of wooden DIY insulated cup???