They should fit inside OK, but you will probably have to move the key-hole type of attachment on the floor. I have a '39 burb and used a set of seats from a '42 GMC, they fit well but since I was making new floor boards, it wasn't a problem to adjust the location of the seat to floor attachments.
Note: the part numbers for the '37's seats are not the same as the '40's.
Good Luck
Stan
