Would that tool affect Jirachi Prism Star or would Jirachi's Ability override the tool's effect?
Jirachi Prism Star's text:
If you took this Pokémon as a face-down Prize card during your turn and your Bench isn't full, before you put it into your hand, you may put it onto your Bench and take 1 more Prize card.
As opposed to the tool's text:
When the Pokemon this card is attached to is Knocked Out by damage from an opponent’s attack, your opponent puts any Prize cards they pick into their discard pile instead of their hand.
I think we'd have to have an official ruling on this to be sure, but it seems likely that Jirachi's ability would win out there. The ability fires *before* you put it into your hand, and generally it's not required that you actually be able to do the thing that it happens before; it's like the steps are:
1. Pick up face down prize
2. Turn it over and look at it
3. Put it into your hand
Jirachi's ability fires at (2). Smoke Baton or whatever it's called replaces (3). The "Before you put it into your hand" is there to prevent people from, well, putting it into their hand (and thus making it possible to cheat), not telling you it depends on that ability to do so.