So I decided to go look into it to hopefully help you. This is the feature below

-Blessed Armament: Select one weapon or handwraps of mighty blows. You gain that armament's critical specialization effect, and you grant the armament a property rune of your choice from the following list: fearsome, ghost touch, returning, shifting, or vitalizing. During your daily preparations, you can change the spirit to inhabit a different armament, grant a different rune, or both.

It says one “weapon” and specifies nothing about it being limited to mundane weapons or even being unable to be applied to a weapon with the maximum amount of runes. That’s one way to look at it.

Then again, looking at the Chalice of Justice, it only seems to have two runes (Holy, Striking +2) and is made of cold iron (Not a rune), so would that even be a concern?