If it were me, I would not cut on it at all. Instead, cut and bend a sheet that would lay perfect over the outside but down inside the recessed edge. Then, flip it over and make several strategic tack welds from the opposite side. This would prevent it from warping and actually make it stronger than the original piece. If your sheetmetal work is on it's game it would look quite good. Wouldn't be a bad idea to use a zinc weld through primer on the two mating sides before you weld it to protect it from any moisture that ever gets trapped.
Best of luck.
I was born and raised on Venus & I may be here a while.....