I'm writing this post with slight embarrassment, due to the less-than-ethical nature of "fishing" with a Neodymium magnet. My Anthropology Professors in college would have scoffed at this idea and given me an earful.
For those not familiar with a neodymium magnet I have included a definition:
A neodymium magnet, a type of rare-earth magnet, is a permanent magnet made from an alloy of neodymium, iron, and boron to form the Nd2Fe14B tetragonal crystalline structure. This material is currently the strongest known type of permanent magnet.
In Europe some people attach these magnets to a metal wire, throw them in ponds and pull out old war items. These magnets are surprisingly strong and can pull up surprisingly heavy objects. Due to not being part of a real archaeological, methodical excavation this method creates items that are "orphans", having no record as to their true location.
But, it could be interesting and slightly more ethical if done properly off the reef at Niku. Due to the weight of these magnets they could be attached to a thin metal wire and lowered into the water until they bottom out. The area where the wire enters the water can be recorded via GPS. When the wire has slack the magnet is pulled up again. To drag it would give faster results, but a less exact location of discovery. Any metal items found would be recorded with those rough GPS coordinates. It does not require a large vessel, only a crew of 2 or 3, a $200 magnet and wire and a lot of patience.
The purpose would not be to pull up the wreckage, but to just indicate a possible location to further investigate. Maybe a starting point. These magnets are strong enough to pull objects up that are covered by silt or a thin layer of rubble. They would also be strong enough to pull up aluminum aircraft wreckage that has just small bits of steel (hinges, wires, bolts) attached to them.
This may be a low-budget exploratory tool.