There is just not the volume of trade between S America and Australasia to warrant direct shipping routes. Most ships go via N America, Japan, Singapore, then onto Australia and maybe NZ - most containers get offloaded in Brisbane or Sydney and are then shipped onto NZ. You might get lucky and find a ship going via Hawaii - but rare as most of the Western Pacific is serviced ex Singapore/Australia.
There might be the odd direct service but it will usually involve either a large bulk load (no good for containers) or something of very high value - and apart from Cocaine from Columbia I cant think of much that would require a charter from SA to NZ.
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