I believe they just ship in a bag, it is the safest most reliable way, I've worked in the transhipping business (Dolphin Int for 7 years) worked as collector and owned a LFS in San Diego (which I sold and is still there). Even when shipping/recieving fish like sharks or abberent colored stingrays, which were worth 2K-3K to the japanese market, and a lot more delicate then angels, they were shipped one to a box, o2 and it took 40 hours flight with layovers, (freight has a lot more layover time then baggage, min 4 hours and when shipping from FL to Japan you go through Alaska which has 10 hours between flts) that didn't count the time from bag to box and international freight rules shipment had to be at airport min 4 hours before flt. After arrival customs/fish & wildlife has to inspect them as well, means some fish were in bags 50 hours, they usually did fine.
Just did a search, to get to cook islands, home of the peppermint angel, you fly to sydney, then next day to Rarotonga (the capital) cost is right around 2K round trip. So far all collectors were forigners, not locals so you have to get someone who can do the dives AND catch fish to go for/with you. Also Scott Michael has a note in vol3 of reef fish, all originally collected fish starved within 6 weeks, and only 1 unconfirmed report of Japanese aquarist that has a pair living.
One other note on collecting deep water, I've collected deep and below 200 ft you have to pop the fish. This is considered safe by some, but all the ones I've delt with long term don't do so well, and I don't go through the side, I use the vent which doesn't actually puncture the fish and doesn't go anywhere near the air bladder.
And I would really like to go on a trip like that 
