That would work. The down side with that is that the cooler will not automatically turn on with the welder. If you ever forget to turn on the cooler and start welding, you will fry your torch cables in seconds. I know for me it would just be a matter of time. A lot would depend on your setup. Like if you have to unplug an move the machine when not using it, turn it off at the breaker, etc. There are a few different ways to get the cooler to turn on with the welder, but nothing is as easy as if the socket was installed on the machine.
Long arc, short arc, heliarc and in-the-dark!