I'd also suggest a plastic bag aroiund the box so it doesn't get too damp, with condensation when you bring it out of the fridge/freezer.

Assuming you get the spider out quickly, then get rid of the bag and make sure the box is in a well ventilated are (even in front of a fan) this will bring it back to room temp quickly and most condensation will be carried away in the breeze.

The box isn't sealed airtight so vacuuming shouldn't crush it, but it will definitely create a negative pressure, I'd probably go with Griffins sticky stick idea though.

good luck