Defensive Beats? Aggressive Parry with a weapon?

[Plane]

Originally Posted by Raekai

It seems like a Parry in GURPS represents a static block with a weapon.
But what if I want an active or striking Parry?
Sure, sure. I could just leave that up to flavor, but I don't want to (unless it's really the "right" option).

The distinction being how doing the unarmed Aggressive Parry (boxing/brawling/karate only) gives you the option to try to damage a weapon, but the built-in ARMED version only gives you the option to try to damage unarmed attackers?