I wouldn't spray the cage. Dampness will quickly cause scale rot and eventually kill your snake. Nerodia need to be kept dry. A water bowl big enough to soak in is good, but the rest of the enclosure should be bone dry. A warm spot from an over head lamp is good. As with any herp, creating a heat gradient is important so the animal can find the temperature it prefers. An under tank heat pad can help withthis too.
Its not hard to get most Nerodia switched to mice. Just choose smallish mice and rub them well with a fish. Feeding pieces of fish will result in malnutrition.