Another place that is added to my knowledge. I have never heard of it before, but after reading the link you gave , I think it is an awesome place. I'm a tourist myself and I would love to travel on Cook Island.
Cook Island is great but I think Cyprus is better because its already stabilized and could handle a lot of offshore businesses or accounts. I think Cook Island is still a raw Tax Haven but it also has a potential itself.
These are required tasks for many of the offshore jurisdictions around. Does the agent you have been using to help you incorporate your business in Cook Islands also do this for you?
But they are headquartered in Singapore so it means they are using a intermediate to do the incorporation there, you may find some︀ cheaper than this.