It has been my experience that modern day radiator shops (if you can find one that is still in business) won't patch aluminum radiators, they want to re-core it or simply replace it from one from their wholesale division. I doubt a welding shop would touch it, they would be scared that they would blow a hole in it.
The Muggyweld looks interesting. I have silver soldered old brass radiators and it held up just fine. The surface pressures inside of a small tube like that are very small and it only takes a good clean repair to make it hold. Since yours is an oil cooler the oil itself may screw things up. I would give it a try however, since you can duplicate the leak, it would be easy to test your repair.
I've seen guys crimp off leaky tubes and it actually worked. I wouldn't do that to yours though, I would never trust it.