I borrowed most all my medical equipment from family and friends, plenty of this stuff sitting in closets.
I used a Donjoy Iceman and bought a Breg pad. Had to swap a connector off of a donjoy pad to make the water connections. I found no risk off frostbite using this, ice bags can be colder, but coverage, mass of cooling matter and avoiding dampness matters. It was very handy for traveling in car, I had an 8hr ride home and the stores associated with gas stations accommodated free ice just by asking.
The Donjoy comes with a 9v dc transformer but will work off of 12V transformer. For use in a car if I had a heavy duty 12vdc to 110vac power inverter I would have used one. I fried a small 70watt inverter that plugged into the cigarette lighter and ended up using a 9v dc car adapter for a breast pump, but a 12vdc should work too, just need the right connectors.
I had swelling down my leg so when I got home and had access to a freezer I was using ice bags too, have a backup!