...occasionally take passengers on-board for a bit of extra cash?
Yacht owners are not generally poverty stricken to the point where a little bit of 'extra cash' in their next voyage is going to be enticing, but they will engage as charter providers because it generates income significant enough to be interesting. For the Cook Islands you would 'reach out' to Australia and see who was providing charters in the south Pacific.
To get started, you can check out Australian Superyacht Charters, where the Cook Islands is on their list. You would use this service to locate a captain who was sailing in that region and sort out the arrangements to bring you on board.
To be really affordable however, you can think about signing on as a crew member for a given leg. To do that in the south Pacific, you can register on the jobs board at Superyacht Crew (again, Australia). Remember there are also port side crew like painting, lettering, decking, and so on which will also help you sign on to a trip in lieu of payment. In addition to the traditional roles of deckhand, engineer, and so on, you may also be able to fill one-off roles like baby sitting, security watch, and translation.
Any methods to reach out to such potential providers?
There are portions of this answer which can be applied to yacht owners. Also, there is a specialist agency in Spain that provides crew members for the Med. They may be able to connect you with a similar agency that works the south Pacific.