Since no one else has offered info or an opinion, I’ll offer the little bit of info I have.
The Chevrolet Master Parts Catalog shows different parts numbers. The parts were the same for ‘37 / ‘38, and change for ‘39 / ‘40. My guess is there are differences in one or more of the following: length, width, curve shape forward and/or aft. Depending on what your goal is, any one of these differences will likely need more than just simple body work.
Maybe someone here with a ‘39 or ‘40 can add info for that running board. I measured my ‘37 and offer these dimensions for comparison.
Length 80” measured from each outside edge. It measured 61” from each inside corner where the fenders meet the running board.
Width from front (forward) corner straight across, perpendicular, and touching the back of the front fender and on to the outside edge if the running board measured 8”. Width at aft corner, again straight across, perpendicular, and touching the front of the back fender and on to the outside edge of the running board measured 12 3/4”.