Just for the "Safety" of it, I would recomend a 20 amp relay. Just run the coil to a standard Plug (No polarity required). As Oldtimer states, putting the relay in a metal box is a good idea, but if the relay is small enough to fit inside, no cutting of the box would be required. Just use insulated crimp-on connectors. (I like solder and heat-shrink, but insulated crimp-ons would be OK.) If the relay only has one contact, connect as you stated. Run the neutral through and break the hot. If the relay has two contacts, feel free to break both lines. Only the Ground MUST be directly connected.
Little Note: Verify the size of the Fuse/Circuit Breaker powering the dishwasher and make sure the Relay can handle at least that many Amps. 20 Amp relays are common and most dishwashers run on 15 Amp service in older homes, but newer homes will have 20 Amp service. If there is a true short in the dishwasher, and the relay turns on the power to this true short, the relay will probably arc weld itself on anyway, but it will safely conduct the current long enough for the breaker to trip. Then it will need to be replaced, but seeing that the dishwasher had to be shorted for this to happen, replacing the relay is a minor concern for after replacing the dishwasher.... (With Home electrical, I always try to think of worst case. If it happens when no-one is home, you want it to handle the problem, no matter what)
If I can be of any further help, just let me know. Also, if I have missed anything that anyone else considers even slightly noteworthy, please comment here ASAP. Better to get all the possible input beforehand. (I'm sure there are specific codes that should be observed, but without getting the exact location, and then reading/researching, I am not qualified to comment on those. I assume the metal box should be mounted, Must be Grounded, have correct cable clamps, etc.)
Good Luck
Art.