IMHO not so easy to TIG...you can't prep the crack with a V, the stay walls are only 0.6mm thick at the top.
Also, the frame should have been silver soldered (certainly not welded), so any melt or internal flux from the nearby fillet between the stay and seat lug will boil out and contaminate the weld.
753 shouldn't be heated above 40% silver temps, 700Cish. TIG or MIG will take it to 1500C.
All the best,
We'll have to agree to disagree
I'd still weld it. You're right though, it is thin metal and won't V very well. If you went over it with a few spots of MIG and let it cool down in between each I don't think you'd affect the surrounding metal. You could quench it with a wet rag to stop the heat spreading but I don't think you'd put enough heat in to melt the solder.