Staking or Peening the square shaft around the hammer is a temporary fix, it can also lead to undesired effects on the geometry of the flintcock’s interface with the tumbler.
Countersiking the tumbler screw is the way to go because it prevents the part from being marred up.
A tumbler screw that is not countersunk will have a very small point of contact, which exerts brutal sheer forces and tears the part up, stripping the threads in the tumbler and gashing parts against a bear surface, in this case the lock plate.
Hammering, bratting or peening a surface in on itself is pretty much the only thing you could do worse.
A counter-sunk screw, on the other hand, has a large contact surface to a cleanly-cut funnel, and the resulting direction of the force is mostly downwards, and you want the force of the contact point to be downward.
The flintcock will end up imbalanced as it was before.
I would even argue that countersigning the tumbler screwhole to be far easier that peening or staking an area around it.