Another option is to just use a computer/monitor extension cable. Either locally at a good computer shop, or from online source. That way you get a nice molded plug and either make your cooler with the appropriate jack, or just cut off the end and wire it right to your cooler/switch. Amazon has a ton of options here is a link to them from 1 foot to 15 feet.
http://www.amazon.com/gp/product/B000067RRX
Also I understand your not wanting to trip a breaker, but having a cooler switch kinda defeats the purpose of having the cooler plugged into the welder. Sure they would go off together, but the big problem is forgetting to turn the cooler on, not forgetting to turn it off. That is a quick way to smoke a torch power cable in short order. I know for me it would just be a matter of time. I would try a new breaker. Nuisance tripping a 50 amp breaker doesn't seem right, even with inrush current. Breakers are made to handle short periods like that, but at the price they now sell them, I would bet that QC on them can't be very good, so try another new one and see if that helps.
Long arc, short arc, heliarc and in-the-dark!