Hi there,
It as absolutely true that there was a "fly-over" of Wellington and Auckland in 1942, by a seaplane from I-25 - a large Japanese submarine. It happened in April of that year - and they were apparently looking for the remains of the American fleet, thinking that perhaps they had come down to NZ after Pearl Harbour.
My grand-father in Wellington heard the plane - in those days a plane engine overhead was a noticable thing - and my father mentioned this several times during my childhood.
The pilot's name was Lt. Fuchida - strangely coincidental as being the same name as the guy who led the attack on Pearl harbour ( Cmdr Fuchida)- and the submarine went through Cook Strait, up the East coast, to Auckland - then off .
It was sunk some time later by American action.
There you go !