Do not put wet ice (regular ice) in with your frozen fish. Wet ice is actually fractionally above freezing and will thaw your fish quicker than you might imagine. If you need more cold, use dry ice, which is well below the freezing point of water.

I also would never use styrofoam-lined boxes unless the styrofoam is chilled in the deep freeze at least overnight. Styrofoam has a high heat index and will thaw your fish if it is not pre-frozen.