There are a number of ways we can recognize a bishop; his mitre is another, as well as his pectoral cross.
The crosier is not a “trinket”. And as to people in the Cook Islands having a symbol other than the crosier, I suspect they will have absolutely no problem recognizing he is a bishop; I suspect they already know he has adopted the paddle as a sign of his office.
It is not like a whole lot of Catholics are going to visit the Cook Islands. And for any Cook islander who is Catholic and has not seen the bishop before, I seriously doubt they will have any problem at all.
If Rome has an issue with it, I am sure Rome can deal with the matter; but considering that the Catholic Church acknowledges other cultures and considers that there may be cultural expressions different than what Europe and North America, I suspect the Church will not have a problem with it.
While I have seen the crosier multiple times over the decades, I would have no problem recognizing a bishop in a Mass or other liturgical celebration if he had another symbol; I might find it interesting or different, but it certainly would not confuse me.
Nor do I suspect anyone there is confused; someone visiting the island might be surprised to see his symbol, but if they have seen a bishop before I seriously doubt they would be confused as to his office; perhaps confused as to his symbol, but not the office.