No, consider the course of the war; immediately after taking Pearl Harbor, Japan also attacked the Philippines, Singapore, Malaysia and the Dutch and French East Indies. In Europe it would have been called Blitzkreig. All thorough 1942 they headed south along the chain of islands towards Australia. Even in December the pacific route was dangerous. The west route put the largest amount of distance between the plane and the Japanese home islands.
You could imagine a southern route Aukland -> Papa'ete, Hanga Roa -> Lima which was probably completely out of any military risk, but there would not have been facilities, most notably fuel.
Right, east across the southern pacific would make sense if there were refueling stops. But in terms of going west they wound up going via Indonesia which the Japanese busy invading, yet Fiji, Kiribati, and Hawaii weren’t being invaded (and Fiji never was, not sure about Kiribati). There may have been naval traffic they would have to overfly they were concerned about I suppose.
We're talking the first 30 days of the war. Singapore hadn't fallen yet, nor had Djakarta. Even though Darwin had been bombed (and my grandmother said that left her convinced that the whole country was about to be invaded) in reality Australia was a long way from Japanese forces. (Of course so was Hawaii).
I was wrong by the way about French Indochina which had been taken after the fall of France.
So hairy, but not as hairy as it would be two months later. They couldn't know that at the time of course, but they had little choice. The only other alternative would have been to stay in Aukland and then be sucked up into the US war machine as MacArthur retreated to Australia.
I can't edit, so I want to clarify that when I wrote, "first 30 days of the war" I meant from the perspective of the plane's crew and most of the regions they planned to fly through.
There were millions in Japan, Korea, Manchuria, Indochina, Germany, France, Poland, etc for whom the war had been going on for years or decades.
You could imagine a southern route Aukland -> Papa'ete, Hanga Roa -> Lima which was probably completely out of any military risk, but there would not have been facilities, most notably fuel.