I agree that whales have become sacred cows, and that it is fair to ask whether the moral ban against hunting them is soundly based. I personally don't think its more morally wrong to kill a whale than it is to kill a cow. But I don't eat cow either, so that argument doesn't interest me. The point is that Whales are endangered, and so we shouldn't hunt or eat them (certainly at least until a minimum viable population is re-established). After that's scientifically established, we can have the debate about hunting. Your proposal to privatise the whale trade would only lead to yet another underpriced natural resource being depleted to extinction. Free market economics has never solved an environmental problem. Markets only work in combination with strict regulation and enforcement against freeriders, which is notoriously difficult in relation to the international commons.
"Free market economics has never solved an environmental problem": emissions trading has sucessfully in the US (see Hahn, Journal Of Economic Perspectives vol 3 no 2 p95-114 for a discussion of this) and is widely feted as part of the Kyoto treaty.
What does it matter if whales are endangered? It will hardly mean armaggedon if we run out. They bring very little to modern society, and propose we might actually be better of without them anyway. The hunters are doin gus a favour, and provifing top quality blubber in the process.
In any case the seas will probably be too hot for them soon and all the dead floaters will be hazardous to our speedboats.