I'm sure that Japan could at least drop some bombs on Yongbyon and majorly screw things up and delay the nuclear program. However, it would not be worth it because it is doubtful that the North's nuclear program would be totally destroyed, and as mentioned before the backlash would be large. When I say backlash I mean two seperate things: Surrounding Asian nations, especially South Korea, getting very angry and the North Korean response in the form of ballistic missles and possibly even DPRK Naval forces attacking merchant shipping. I can see that happening.
Anyway, the US is the only country that would attack that has the capability to destroy the North's program throughly. To accomplish that effectively, the US would probably have to mount multiple attacks, targeting Yongbyon, North Korea's nuclear-capable missles, hidden nuclear facilities and possibly air defence targets. So Japan does not have the capability to accomplish that sort of thing.
Other than an airstrike, Japan does not have many options. A commando strike would not be worth it, as you could not take out the North's nuclear program with one commando raid (unless you landed commandos in many locations, all of which heavily guarded, etc. That's not feasible). And isolating the North any more is not really an option. It is so isolated already that a naval blockade or something like that would not have an effect.