Normal copper sheet isn’t oxygen free, probably has zinc and stuff in it too so won’t TIG well. If you do try to weld it use a respirator, the fumes are gnarly. Better brazing if you can.
I dont know if brazing is possible on thin sheet, you'd have to heat it up a lot before you can braze surely and then in turn setting the wooden base it will sit on. I've not crossed this bridge yet but when i dont im sure brazing is out for sure.
Spot temperatures will be lower with eutectic brazing rather than welding though. Either way, it's going to warp unless you have heatsinks, massive fixtures, and a welding/brazing God.
Normal copper sheet isn’t oxygen free, probably has zinc and stuff in it too so won’t TIG well. If you do try to weld it use a respirator, the fumes are gnarly. Better brazing if you can.