The only issue as a counter to that IMO is how would such an injury manifest itself? The mortal is injuring flesh, the god is injuring the "mana" of the other god.
Is it truly the arm of Agrik that is injured? Can Agrik shapechange? If he can, are all of his physical manifestations wounded in the arm as well?
IMO the greater gods have many manifestations that exist at the same time and injury to one would not extend to the others. (IMC demi-gods have only manifestation but may change shapes.)
If you are just talking about one of many manifestations or the only manifestation shape changing then the other shapes are the same manifestation with the injury. If the ability to shape change is relatively unlimited the injury might not be to the arm and might only be represented as a lessening of the aspect's mana. But IMC most gods are not unlimited shape shifters and have a number of forms they commonly take and may specialize in. If a god had two forms that had similar parts - say changing from a bat-winged demon to a wolf - then an injury to the arm of the demon might show up in some form on the wolf form. However, if the shape change was fairly extreme - say from a bat winged demon to a talking flame - then the injury might be unobservable, only be in amplitude of the flames or just in mana.
When changing forms if the god was consciously concerned with obscuring the injury obviously it would not carry through. Even in the same form the god could seem to heal the injury but could still be reduced in mana. But if they weren't concerned/paying attention, or the GM just wanted to give the players a clue, a signature injury might carry through to other shapes they may take.
The mortal is injuring flesh, the god is injuring the "mana" of the other god.
are all of his physical manifestations wounded in the arm as well?
That is a good example. When I was thinking before about the difference between a mortal weapon striking a god vs a godly weapon striking a god a mortal wepon might cause just cause physical injury while a divine weapon (even in the hands of a mortal) could also strike at the mana of the god.
While the theoretical possibility of a Valar/greater-god weapon that would not only injure the physical and mana of a single manifestation but would also injure some/all the other manifestations of the god. In that case - perhaps including the example of Larani striking with her sword - all the aspects and manifestations of Agrik would be injured.
It would also make sense in healing of injuries. Repairing simple physical damage as would be caused by a mortal weapon would be trivial to any god - even mortal spells like regeneration would work. Repairing damage to the god from divine weaponry though would be beyond such spells - even if they covered up the physical damage the injury to the mana would remain. A divine healer such as Peoni would be able to heal the damage or resurrect the slain aspect of Larani which not mortal spell would work.
What about a mortal struck by a divine weapon? It might be healable by normal means, such as Shek-P'var spells, but if the damage is more than physical - striking into the spiritual essence of the mortal - then the injury might not be healable by mortal spells. Even if the physical damage is fixed there could be lasting or even incurable mana injuries - perhaps like Frodo Baggins with the injury from the morgul blade that, despite all the healing skills of Gandalf and Elrond, would never fully heal.
A class of injuries and (reason they exist) that are resistant to Shek-P'var healing spells is kind of needed in HM - as something that is extra scary. Maybe priests can heal the injury when Shek-P'var spells fail, maybe not. Perhaps magic or holy/unholy weapons that prevent normal healing and/or magic healing.