So this rune is awesome in concept. Chainsaw swords! It deals slightly less damage than an elemental rune but also punches through resistance and hardness better. But I have questions.
1) Do Versatile S weapons like the shortsword qualify as "slashing melee weapons" that this can be etched on?
2) Does the Interact action mean you need a free hand to "rev" the weapon up to d12?
3) If that's the case, can you regrip the weapon in two hands as part of the interact action?
If the answers are no, yes, and no, that leaves a very narrow range of weapons this can be used effectively on. Requiring a free hand to activate means two weapon warriors won't be interested, and if you can't regrip as part of the action than neither will two handed warriors. So this becomes a rune for free hand fighters with slashing weapons.
From my understanding of the rules: no, no and no.
1) RAW would be no, from my understanding. A shortsword is a piercing weapon that happens to be able to deal slashing damage because of a trait.
The language of Versatile seems to support this, saying "a piercing weapon that is Versatile S" in its example, suggesting such a weapon is still a piercing weapon and just happens to be able to deal slashing damage, rather than a weapon that's both.
2) I don't see anything in the ability's description that suggests you need a hand free. It instructs you to "brandish" your weapon and nothing else. Interact actions require you to 'use your hand or hands to manipulate an object' ... you already have your hands on the weapon, though.
3) But no, Regrip is its own separate interact action, if you only had one hand on a two handed weapon you'd need to spend another interact regripping.