> You could, and should, do both of course.
No, you should just use the truth, since the lies combat the truth.
If you prevent mislabeling, the rare fish becomes expensive rather than cheap-and-adulterated, the price differences drive lots of the people that think they prefer the rare fish to settle and try the cheaper, less rare, fish, and to the extent that the cheaper fish actually is suitable, people learn and it becomes popular.
If there is a risk of this transition happening too slowly to meet some social good (like, preserving the rare fish), you enact appropriate protections to the rare fish (either quotas, taxes, or outright bans) that restrict the supply or drive up the retail price, which accelerates the process of conversion.
> It also eases the transition from tuna to other fish.
No, it actually delays the conversion of demand by masking the cost and delaying people trying the other fish as itself and learning that it is acceptable.