As Weapons Officer on a 637 in the late 1960s and early 1970s, I did everything to avoid carrying MK-16 Torpedos.
The Non-nuclear weapons of choice were the MK-14 against surface Targets and MK-37 With and without wire guide against submarines.
You are absolutely right about with the Soviets developing more Nuke Boats, the MK-37 became less attractive and less effective.
The MK-14, with all of its problems during WWII, was a reliable weapon in the 1960s-1970s.