Such moves by North Korea are a perfect icentive (or a pretext) for the Japanese to start getting busy militarywise (including the nuclear weapons).
North Korea will not stop giving pretexts anytime soon, and the actual threat to the country will remain minimal, so it only makes sense to go steadily in one direction. To give another example, let's say Putin was interested in warring against Turkey, and so used the friction between Turkish and Russian military missions in Syria to escalate tensions over the next year up to a logical formal declaration. Indeed, wars between states tend to come about through measured escalation rather than sudden outbursts.

For Japan to use the North Korean test to abruptly justify full rearmament and a nuclear weapons program (and at the very least the domestic outcry would be at least as big as the international one toward the latter) would be like Putin having responded to the downing of his bomber by declaring that Russian missile bases were to be armed and ready to launch at Istanbul. Also notice that Germany has recently committed fighting forces to the Syrian mission, likely in response to France's sudden martial assertiveness. Doesn't mean Merkel's about to declare herself New Holy Roman Empress anytime soon.*

Similar ideas were expressed about Russia being unable to sustain a military campaign at the prospect of economic santions (or with them enacted), but Putin has opened a second one in Syria while continuing to support separatists in Donbas by various means. And Japan's economy is much more powerful than Russia's.
Well, that's the idea. To simplify a bit, Russia's economy is commodity-rich, while Japan's economy works on the import of commodities and the export of consumer electronics, advanced machinery, complex instrumentation and software, etc.


*Just as an example; no one wants that, least of all Merkel.