The only big problem with a mig weld is the lack of control. You will probably deposit more weld that you actually need but so what. There are a couple of things that you should do to get satisfactory results. Take some thin aluminum sheet and cut a hole to just fit aroung the barrel hook. and wrap it around the barrel to protect it from sparks. Beer cans work great and the hole can be cut with a utility knife. I would use two layers of the aluminum since they are so thin. You also need to drink two cans of beer first also. I would then pre-heat the hook surface to only about 150 degrees. Be careful that you do not get the area to hot or you could soften the solder joints. Then have at it with the welder. I would keep the heat up just a bit and the wire feed down just a bit and simply spot the weld in a spot at a time making sure to keep an eye on the overall temp. If you can not quickly touch the surounding area with a bare hand on and off you are getting it to hot and need to stop. Keep the barrel in a good position to let gravity help flow the puddle where you want it. Also very important is to clean the area with a solvent before you start. If you get any purosity it will be a nightmare to get rid of. Good luck.
Bill g.