Lifou is the only island you can complete formalities in The Loyalties but you can stop at any other island if you follow the correct procedure. (Thanks to Heather on Aradonna for the information).
1. Send an email with your request to email@example.com
2. Specify which island you want to stop at, give your boat name, POB, and onward intentions
3. You will get a reply. Their tel if you speak french is (687) 26 53 00 or 27 64 97
When you arrive visit the local gendarme and make sure you fly the yellow Q flag the whole time.
4. Then proceed onto Noumea, if New Cal is your destination.
Please note that you need to keep the authorities informed of any changes in your plans. This applies to all countries actually, and as long as they are informed you will normally find them accommodating. In particular New Caledonia officials are very familiar with the maritime world and what can change on route.
I checked the above email address and although I got a notice about it not going through, about 5 mins later I got a reply to say it was correct. I was also sent sent two attachments that cover this information. Received 6 Sept 2017. Yit Mike will put these on soon. It is in .pdf format and at this point I cannot add them. Done, thanks Mike.