The 1936 cross-shaft is mounted on the front of the frame X center, so is closer to the front than is the 37-38 cross-shaft AND the lever for the link from the floor-mounted handle is on the RIGHT side of the transmission, whereas on the 37-38, the lever on the cross-shaft to which the cable attaches is on the LEFT side of the transmission. The cable from the under-dash handle on the 37-38 runs down the inside of the firewall (behind the insulator) and under the toeboard and to the right and then down the LH side of the transmission, back to the area of the u-joint cap, where the LH bolt that secures the two halves of the u-joint cap also has a provision to secure the rear of the cable housing.
You will have to reroute the forward cable to the RH side of the transmission and fabricate "something" to secure the housing in the proper location and then attach the rear of the cable itself to the cross-shaft lever. The length of the cable will be critical; Ford made several different lengths that you can choose from, OR you might have to make a custom-length cable with the threaded ends to which the adjustment yokes attach, and then the yokes to the handle and the lever on the cross-shaft. The yoke that attaches to the handle is a special long-reach to
clear the handle workings.
IF you were to use the original 1936 rear transmission mount (evidently you are not?) on the side-shifter transmission you could leave the handbrake handle in the original location (the handle ratchet mounts on the transmission mount) and have no problems...unless you are wanting to eliminate the floor-mounted handle?