I'd say you get to choose which power applies (Cogsnap's or the Alchemical Kit's)
I was actually just going to pose this question, but with Damiel. The ruling I'm trying to find and have been unable to, even though I swear I saw it in the rulebooks somewhere (I must be blind), is which cards override which. I feel like it had something to do with locations overriding scenario cards and the like, or something to that effect.
That would be the Golden Rule, at the bottom of the first page (technically page 2 since page 1 is the cover).
Which brings me to the way I was reading it: is the card more specific than the power, and therefore does the alchemist's kit override Damiel's own power, making the alchemist's kit a drawback instead of an aid; in most cases, I'd rather recharge the card, but the kit seems to imply that it's always discarded.
I designed a game once that uses the "when you would" language, which in my game interrupts all other sequences for that effect, but there's still the matter of which effect/power triggers first: the card's or Damiel's innate ability.
Opinions?
There is no overriding, because we also have the rule "if the game doesn't specify an order for things, you decide the order" (p29 of WotR rulebook). Both powers would trigger at the same time, and there is no defined order as to which applies first, so you choose the order in which the powers apply. Since the powers are also mutually exclusive, doing one precludes you from doing the other.
In any case, even if you did rule that the cards were in conflict and therefore the Golden Rule applied, the Golden Rule states that character cards would override boons and banes.