Nobody would ask the Russians or Vietnamese to surrender their rights. If they are party to the agreement (as I'm sure they would want to be if they value international trade in other goods), they would get shares enough to represent their rights. Negotiating who gets what shares will be a tough battle on all sides, but it will be waged at the table and not at gunpoint.
As soon as Russia owns its fraction of the world's fish, its attitude towards exploiting it will change completely. That's the way it is with ownership.
Your assertion that the Vietnamese must max out their catch in order to survive is wrong. Even in the worst-case scenario, at some point it would be to their economic advantage simply to sell the shares and stop fishing, which is a big improvement over the "stop fishing" scenario they will otherwise face. Right now they max out their catch not because there is no alternative, but because it is the most economically attractive alternative. That can be changed through ownership.
The process of granting land as property in the U.S. was indeed a painful process, yes. But you must agree that SOME process to do that was absolutely necessary. If it hadn't been done, the U.S. would be a barren mud patch by now. I'm hopeful that the granting of ownership to wild fish stocks will not need to be that painful, but even if it is, it is just as necessary.
If we let industry take the lead (not the lawyers) I suspect the need for granting stakes in wild fishstocks will not ever become necessary. Corporate farming will likely grow at a pace sufficient to avoid such drastic measures (unless of course the government induces some radical imbalance in the process due to fear mongering, politics, and lawyers)