If its chromoly, the tube is heat treated and tempered, but there is no post weld heat treatment. There may be some post-weld stress relief (heating to below the temp for heat treatment) but mass producers (and good custom builders) have the jigs set up so precisely, and the mitering done so well that the PWSR required is minimal.
In any case, heat treatment and tempering for "bikely" chromoly doesn't leave them too hard. HRC 20-30 IIRC. A good hacksaw will work. Given how thin wall the tube is, use a fine (32 tooth/inch) blade or the tube might stick in the blade gullets. Your idea to use a straightening jig is likely a good one (depending on how well you implement it!
) If this is a threaded fork you'll have to clean up the end (square it and deburr it). I'm assuming that you are cutting in the midst of the threads, and not in the unthreaded area. If the latter, you'll need to cut threads on it. You may want to have the LBS do that as the die and die holder/centering fixture is expensive for one-time use. But if you are cutting a threaded fork in the midst of the threads, you'll be well served to thread on a locknut before cutting. Run the locknut down closer to the crown than the cut. Make the cut. Clean up with a grinding wheel (to get the end square and flat) and a Dremel tool (to deburr). When that's done, unscrew the locknut to chase out the thread ends a bit. This will allow you to thread stuff back onto the cut fork more easily.
Can't recall, but I seem to remember that if you do need to cut more threads on the fork you do this before cutting. This automagically centers your die nicely.