So basically, I just duplicated the Archon's attack, including the actor and damage effect, changed its attack damage, attack rate, and range. I stuck it to an air unit and it mostly works. The only thing that doesn't seem to work is the graphics. When he fires the shot, it makes the sound, the damage is dealt, but I see nothing. Now, what I want is for it to not have the beam, but only the impact locations graphic. Is this attached to the units model? Or am I missing something?

The impact model actually seems broken for me (wtf eh?). But the model itself is Archon Attack Impact, you could try creating your own actors using this model for your weapon. There is probably a way to fix this but I don't have the time to look at it right now, I will take a look later.

Try Duplicating each part of the weapon in this order:
Model -> Actor -> Weapon

Duplicate the model (presumably Psionic Shockwave [Model] Copy) then manually apply psionic_shockwave.m3 to it under "Model"
Then duplicate the Actor and check the sound boxes (not the model boxes) and when you are done, edit the Actor and go to "Model" or "Art - Model" and apply "Psionic Shockwave Copy"
After that, Duplicate the Weapon and its effects (but not the actor or model, cause you already made those), and then apply the previously created Actor "Psionic Shockwave Actor Copy" to the weapon, after that feel free to go about and edit the effects.

Hope this helps, I haven't tried it but I think it works, applying the actor may be under the weapon or the effect, but this'll give a general idea,

-Mp)Cheese

I could have bombed this if there are multiple models, if there are, then repeat the duplicating steps with the other models and their respective actors.

Or, if I'm completely wrong or unreliable, listen to Temp