Wizkids Rules!

Can I choose to shuffle the face down damage cards assigned to my ship or must I keep them in the order they were assigned?

For example, if my opponent has the Gorn captain Lahr, he can "Choose 1 facedown damage card on the defending ship. Flip it face up and resolve its effect." Am I allowed to shuffle my facedown damage cards before Lahr gets to pick one?

No, you may not shuffle your damage cards unless an effect tells you to do so.