My new hand isn't the greatest either... Still, it should be sufficient for our needs at the moment. I will choose the first option. No cards from me whether we're trying to pass this or not.
Even if you have a Political Prowess, I would still rather pass the check - since then you don't have to waste your next action to get out. Throw it into the check if we need it to pass.
EDIT: My turn is next, correct? Actually I strongly recommend failing the check and sending me to the brig if we want to conserve cards. I would be burning a powerful card to get out, but it would be by far the cheapest way to pass this check.
Even if you have a Political Prowess, I would still rather pass the check - since then you don't have to waste your next action to get out. Throw it into the check if we need it to pass.