Weld or braze, either is fine. But tapping afterward is difficult if brazing and impossible if welding. You want to retain the micro-adjust so pre-set the right side to where you want the wheel, and lock it in place during the braze or weld. Then you can adjust wheel alignment from the still usable left side.

If you opt to braze, Yellow Jersey does excellent work at reasonable prices, but brazing will burn paint off the stays for a short distance. OTOH, any decent auto or motorcycle mechanic can weld this properly at a reasonable cost, and welding won't burn paint off beyond the immediate area, so may make a prettier repair.