If you use the US post office, and ship 24 hour guarantee, if they are even a few hours late, you can recover your shipping cost. The person getting them would need to sign at the time of arrival.
There is also airport tp airport, which allows you to ship lots of weight for a fairly reasonable price. But you would need to to drop them at the airline, and your customer would need to pick them up at the airline office in his/or her area.
You would need to contact airlines to see who flies where you want to go, and what their rates are for what you have.
A good way to find out, is to fill you bags you are going to use with adequate water, and weigh them, in the box, then call all check rates for that weight.
When I have shipped 2" fish, a 5 lb box usually goes for around $60 at the post office.
I would venture to guess your fishes weight will be 50 to 100 lbs.