This time can be stretched somewhat by filling with oxygen, rather than air. Put the bags in a padded, compartmentalized container, and ship by air. For larger fish, or longer trips, one can use a sealed bucket for each fish, rather than a bag. Fish won't eat during the move. They're too stressed, and you don't want to degrade the water quality by the food, anyway.
Fish can survive a week or so without food if they've been previously well fed.
Try to maintain an even temperature, perhaps by placing the fish in a sealed cooler, or compartmentalized cooler. After the move, slowly condition the fish to the new tank location, as you would in adding new fish to a tank. You've read all the FAQs, found out everything you can about diseases, ailments and the proper treatments, asked for help from several knowledgeable sources and have come to the conclusion that you cannot nurse your fish back to health. And since you took on the responsibility of caring for the fish you now must find the most humane method in helping it to die. Several options exist for euthanizing your ill pet.