As far as a "direct replacement" goes, that would mean that you have to take the 1939 light switch into consideration which is mounted on the bottom end of the '39 steering box. If you can live with moving the light controls to a conventional switch on the dash along with a foot-operated dimmer switch, I would look into seriously replacing the '39 box with a Saginaw 525 steering box like was used in earlier Cutlasses and Chevelles as well as others. They are only slightly larger than your '39 box, and will likely give you much more of a feeling of power steering. Not only that ..... your '39 Pitman arm will bolt-on like it was made for it. BELOW is a picture of a 525 box in a '40 Ford for comparison .... looks like it grew there!
You might consider having someone like Neal Jennings nhrp32@att.net rebuild your stock box. He's a California guy and one of the best. I have a 525 Borgenson box mounted on a P&J's bolt on frame mount in my 40 coupe and it drives great. Kinda depends on whether your trying to maintain originality or up date to something newer?