Oh hush, there are still plenty of options for keeping everyone happy.
So we want to keep the ship, and have Hanako not get demoted.
Charisma is still intact, and there is still crew on the ship. The ships seemed pretty confident that it was just letting itself be taken so that it could find these pirate's base. Since the ship could escape on its own at anytime there doesn't seem to be much of a reason to order the self-destruct. At the very least they'd order the ship to try and shoot its way out before trying to self-destruct.
On the other hand, if the decision to order the self-destruct is going to happen then we still have some time before command makes that decision. It is time for Hanako and the others to call in what favors they have in the SAoY to keep the ship from getting exploded. It also doesn't make sense for them to order the self-destruct before they have an idea of what is going on (A single report from a SAINT operative shouldn't be enough to start triggering auto-destructs! That usually requires 2 officers at least!) so we should get a few rounds of talking with whomever is assigned to review this operation before they explode the ship. This is a good opportunity for someone to pull some lawyerin' and get command to sign off on Hanako's plan to trace the ship to the pirates.
Finally, maybe they do decide to blow up the ship. If the pirates are half the pirates they think they are they would have managed to disable the auto-destruct by now: Either by frying the computer, shooting the reactor out of the ship, and/or cutting off the engines. The Eucharis might end up pretty worse for ware but it will still be savable.
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Bottom line, Hanako's plan was to let them take the ship. Since everything is going according to plan, it doesn't make sense for the Star Army to immediately blow up the ship and the remaining crew. We still have a ship to save (even if it gets blown up, we still should go recover what is left) and the crew still has plenty of options for getting out of this jam.
Maybe have Hanako break down and cry a bit, let the rest of the crew take this one on.