We sailed around the world with Dufus....our Rainbow Lorikeet. Be sure to check out of the US (which is not required by US Customs) and have your birds listed on your manifest. When arriving in foreign countries, be very careful to be sure that they list the birds as entering.
The risk with taking any pets to a foreign country is that you must abide by that country's laws (which are subject to change at
any time). The big risk is if one of your birds gets away. You could be held in violation of that country's law. Be sure that you understand what the consequences are. It could mean forfeiture of your vessel, in some countries. Be particularly careful in New Zealand and Australia.
In New Zealand, we were required to have an inspector come on board once a week. If we were in some far flung place, we were responsible for the inspector's's transportation (that was 14 years ago).
BTW, from my experience with experience with Cockatoos, I will just guess that you may not be very popular in the anchorages. Also, I can't tell you how many times I had to go up the mast to get dufus out of the rigging. I'll bet the Cockatoos will be worse.
He's fallen overboard a few times while messing around but he learned to splash his way back to the boat........then, of course,
he'd be mad at
me.