Cold water is used in operating a disposer so that fat particles solidify and are chopped and flushed into the sewer system. It is estimated that under normal conditions, the average person uses 1.5 gallons of water per day to operate a disposer. Remember that waste food disposers are made to operate with the water running. Operating the machine without running water will ruin it. If you are serious about not using water, then dispose of food wastes by other means.
Careful planning can help eliminate some of the waste from the start.
One way to simplify cleanup is to peel vegetables, eggs, or other food onto newspaper, wrap the paper around the food waste, and then dispose of the package in the garbage container. This saves you from scraping peelings out of the sink or off the counter after the preparation job is done. It will save water because you don't have to operate the disposer. This might be a good time to consider starting a compost pile if you have available outdoor space. As an emergency measure, store drinking water for short periods of time.