In this case it is not the species being driven to extinction, it can be farmed, it is the species being driven to extinction in the wild. People prefer wild sturgeon caviar to farmed caviar even if they can't tell the difference.
Perhaps you could solve the problem by making it illegal to identify caviar as wild. Of course criminals would always try to supply the demand for wild caviar but they could just open a tin of farmed caviar and would as it would be cheaper and they wouldn't care about defrauding the recipient.