I had always understood a wake to be an event that takes place before a funeral that acts (primarily) as a social gathering. Especially in Celtic/Irish tradition (or so I read), the emphasis at wakes is on celebrating the life of the departed; dancing apparently takes place at wakes in some cultures, though never one I've been to. Given that context, I think that interpretation of wake makes sense.

As for "shoot the cat," as best as I can find it means to vomit profusely, especially because of liquor. Not exactly clear on the context in that situation, but if they've been celebrating a little too much at the wake, "shooting the cat" is definitely a possible side-effect.