The only way the UN could stop Japan from Whaling, is to outlaw it and enforce the law. Send a few warships take a strong stance, even if it means boarding and capturing a few of the Japanese whaling ships, if they show they have the will to do it Japan will back off.
Its A lot easier to ignore a few activists boats, than it is to ignore a ship capable of sinking you.
But in reality, the Nation/Country's Waters that the Japanese are whaling in can do the same without minimal input of the UN. Just none of them our willing to risk losing trade with Japan or cause a diplomatic incident on behalf of whales.
Japan overall has always been into whale hunting regardless of the International outcry, I don't think the UN has the sufficient power or backing to impose any meaningful sanctions on Japan to curtail this activity, so overall I don't believe that the UN can force Japan to stop this activity.
With so much press over the indiscriminate extermination of whales and dolphins by Japan, I believe that if they had any intention of stopping that they would have already done so. It is far too profitable of an industry for them to just up and quit suddenly. I feel like they would gladly pay any fines necessary to continue their exploitation of these animals.
Before you start counting your whales, so to speak. It should be noted that Japan's scientific whaling program in the North Pacific, JARPN, is not effected by this ruling and will continue. In addition Norway,
Iceland, Greenland, the U.S. and Russia are also hunting whales. So, whaling is far from over. And, as Professor Rothwell pointed out, only JARPA II is effected by this ruling. Japan is perfectly free to start a new research program in the Antarctic. Not to mention the fact that they could simply leave the IWC. In which case they would no longer be bound by the moratorium banning commercial whaling.
I do not think that the UN will be able to stop Japan unless the public opinion changes on them severely. The Un doesn't really have that much power to do anything other than expose what is going on and help to create world wide outrage from people and environmental groups.