Reading the report, the crew did have fuel for a diversion to Noumea between approx 0905 and 0930.
They had 3 Speci reports (2 in this 25 minute period), each getting worse. Once the first Speci was received at 0800 indicating that the weather at LHI was not as forecast, the process to assess the actual weather at Nandi and Noumea should have started. This should have been the main focus of the crew for the next 90 minutes up to the PNR for Noumea.
As the weather at YNSF was deteriorating from the Specis received during this period, 90 minutes is more than enough time to determine the time and fuel required for a diversion to Noumea.
The crew state that they were not sure of the winds to Noumea. They were in the position of flying in the actual wind. This was probably more accurate than the Grid Wind forecast, if they had it.
It appears no request for the weather at Noumea was made. Why? This would be the first thing asked for once the first Speci for YNSF was issued.
As we are not informed of the weight at departure, we do not know how much extra fuel may have been carried and if that extra fuel would have allowed an approach at YNSF and a diversion to Noumea.
One thing that was not raised is the need for a Company to require an alternate when planning to a single runway airport, especially a remote destination. The Westwind is above the weight allowed for 04/22.