Anders;
Most race car and aircraft builders who use chrome- moly tubing use it in "Condition N", normalized. The weldment doesn't need to be heat- treated if it is welded properly. Gas welding spreads the heat over a wider area so the joint has less built- in stress than a TIG weld. TIG is fine, though, if it is carefully done.
That's an interesting project you have there.
Regards, Neil Tucson, AZ