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Bending brakes is usually for making them larger, not smaller... when you shrink brakes it leaves them with horrendous long legs that are just begging to get caught up and broken.
Personally I would hit up Rossignol/your local shop and try to get some narrower brakes from them.
But failing that, sure, a good tig weld should be just as strong as the rest of the metal. Just remember that everything involved will get hot as f*ck so it may melt the feet of the brakes a bit. If you want to do it nicely, grind the 2 halves of the join for either a single or double V (so they're like \ / or > < ) so the weld doesn't sit proud.
Good luck finding out the metal involved so you can choose a filler rod though :/