I've picked up my packages from the airport a couple times. You'll need to let the recipient know the airway bill number just in case the authorities demand for it.
I have a few times. Its more expensive but safer because the fish are usually only boxed/bagged up for 6-8 hrs. Compared to overnight shipping where they may be boxed up from 24-36hrs.
Most supplier box the fish up and drop them off the evening before they actually leave for shipment. In cold whether this makes a big difference.