United Airlines fly to Majuro 3 days a week in a B737-800, so the airport is more than capable of handling an A330. RNAV approach both runways. As good as an ILS.
If the airport is classed as Cat C, not suitable, then why bother nominate it as an EDTO alternate. It's your licence. Why would you fly on one engine, further than you had to do so, over nothing but water.
The passengers wouldn't be happy if they knew they were being put at extra risk.