I wonder what are closest significant shipping/flight routes of Nemo

Likely not much, if you were to go further south, there are a few parallels/latitudes where no landmasses exist. This creates a very hostile environment for maritime vessels due to 90mph (150kph) westerly winds and 50ft (15m) waves. As for planes, most east bound flights from AU/NZ, the great circle route that runs through there doesn’t really go anywhere except to middle Atlantic Ocean, dipping south of Cape Horn. It is a place truly devoid of people.

If I recall correctly, they are actually planning the deorbit of the ISS to land around there precisely because of its proximity to literally nothing.