If this card gets destroyed before its Enter trigger resolves, you must still resolve the Enter trigger and add an [Addition: Resonator] card to your hand. Thus, while you may choose to fail to find, you must still shuffle your deck.
There is no priority window in between searching for an [Addition: Resonator] and placing it onto this card. Thus, a player cannot cast "Stoning to Death" on Athos in response to their opponent attaching "Crucifix" from their deck to this card with its ability.
The added [Addition: Resonator] does not target this card as it is not being cast.