I think you should allow for Bonaire, Sint Eustatius, and Saba as type'ins for Caribbean Netherlands. Also, I'd add a few type-in so you don't have to type islands every time.
Unlike Curaçao, Aruba and Sint Maarten, which are countries of the Kingdom the Netherlands (together with the country the Netherlands, which is the only one of the 4 to be considered sovereign)
And could you accept US Samoa for American Samoa?
Also, having some sort of hint, like what continent they are associated with (could have "none defined") or who currently controls them (could have "disputed") would be helpful.
Swahari Republic/Western Sahara
Taiwan (can't join the UN, can't fly its flag)
Wales, Scotland, and Northern Ireland (reference source, FIFA)
And so many others
Sorry but for me, it's a question of basic understanding of geography, and there are more ambiguous cases than this one. The French overseas departments are constituent parts of France, have very few autonomy, apart from that needed due to the distance with the mainland, and have very little chance to become independent soon.
Note: pretty sure Svalbard is in the Arctic Ocean though
Anyway, cook idea for a quiz. It seems to be substantially a matter of naming the overseas territories of the UK and France.
--> Aland Islands, which is not integrally part of Finland
--> Ceuta and Melilla, which are enclaves within Moroccan territory and enjoy a special status
--> Easter Island, which at least on a cultural level is far from being considered akin to the rest of Chile