Tig-welding and THEN heat-treating O1 / A2

Sounds like clicker dies or steel rule dies, both of which are made by bending and welding strips of tool steel to shape. Both are inexpensive to have made to order. What are you cutting?
Ned Simmons

We use a filler called "G2" for full-hardness applications like trim edges. You have to beat the weld *immediately* after you've laid it in order to stress relieve it, or it will likely crack.
This filler cannot be heat treated after it is applied. Also, whatever the weld is on cannot be fully hardened, only flame hardened.
I'm not too sure about tig welding tool steels together though. I'd imagine you'll end up with the area around the weld being very hard, and they areas away from the weld still being soft. O1 would be more likely to crack during subsequent heat treatment because of the more rapid cooling. I'd start with an air hardening steel like A2.
It'll probably work unless you want a hundred thousand hits out of the die... Best thing to do is... Try! :)
Regards,
Robin