As you all know by now I have a bunch of junk actions and don't Know squat but am moving towards knowing squat, that's why I'm here.

So, I have another '96 that has but only four threads available at the aft end of the receiver ring. I also have a barrel that has four serviceable threads the same, at the end. Is that enough?

What make of 96 action? I have barreled Browning actions from the 1960's with very thin receivers and 4 or 5 threads and never had a problem. The military actions very in the type of steel used.

That is sufficient.
The only 96 Mauser action I know of is the Swede and that is what the OP has.

FWIW, on a theoretically infinitely long bolt, the first thread takes a third of the load, the first three threads take three-quarters of the load, and the first six threads take essentially the whole load.