The grains will barely notice being mashed in the cold. Those coolers are well insulated.
For chilling, why don't you just get the garden hose out? The water will be nice and cold, making chilling a breeze. Otherwise - during the summer I fill my HLT with water and ice and run that through the chiller. Once at an event without running water, I did the same and used a small pump to pump icewater through the chiller and back into the ice.