Thematically, short swords from this era were mainly thrusting and hacking weapons.
Infantry from military organizations such as Roman military or Spartan military would pair these weapons with a shield, hacking and thrusting around the shield at exposed areas, such as a neck or limb.
Because of this method of use, there were often severe injuries that were not instantly lethal, but injuries where profuse bleeding occured.
So, if blunt weapons such as a mace cause secondary effects such as stun and axes cause similar I propose...
DoT. Very quick activating, perhaps 2-3 tics, and this is where the bump in damage is.
So, defininetly increase damage, perhaps a straight bump for some attacks, but perhaps some have a fast burst DoT. Adds something unique and period specific to the set