The inner lock mechanism is entirely independent from the door handle key, that's why whenever it was fitted (before 1970) to the front passenger door, there was also no key barrel on the push button, and driver's lock was always actuated only from the outside.
In theory you can fit a push button from a post-70 car to a pre-70 lock mechanism, you will then be able to lock both from inside and outside, but should the inner lock be activated, there will be no way to unlock the door! I would do it a different way: keep the passenger door locked all the time - it can always be opened from the inside as you may have noticed - and lock the driver's door with the key through the window, sitting on driver's seat. Of course, you must be careful not to get out of the car without the door key.
