Yes the 1937 head will fit a 1939 bock just fine. Should even be the same casting number. Keep all heads, even the crusty ones as they can and will crack so spare have value. Keep the lifters numbered and matched with rods if you can.
A quick clean of the bottom end and shim adjustment on the rod caps might be all you need. These engines are pretty durable.
A head job may not be as bad as you think once they actually clean it up. The head was regularly serviced back in the day as part of a refresh and the valves are readily available. Both versions of the pilot bearing are available new as well and are cheap so you might be able to mix/match with your trans input shaft.
Last edited by canadiantim; 12/21/2020 11:59 PM.