leaving aside the logistics for the moment, one variant could be to have additional ship specific damage decks
usage could be:
a) the specific crits are triggered by cards from the original deck, either by redefining some of the originals as crit stand-ins or by using the second hit from a double as trigger for something specific. (something along those lines)
one deck, mostly the original plus some extra cards for the ships
b) the original deck stays as it is, the specific decks for the ships exist in parallel and at a crit you choose from one of the decks. Here the original deck can be kept completely as is, and you only have to add the other decks. The challenge here is to balance the decks in their severity.
both cases would just mean you would have to supply the new decks in some form.