The card for the ION Cannon battery available to huge ships says that it deals one critical hit. Does that mean that if the defending ship still has shields it can negate the face-up damage card required for the cost of one shield point? Am I correct? To me, unless the card says deal one face-up damage card, then the defender's shields can withstand the hit.

Yes, you're correct. A ship that suffers 1 critical damage removes a shield token if it has any shields left.

To me, unless the card says deal one face-up damage card, then the defender's shields can withstand the hit.

Yup, things that deal cards avoid shields.