The patch notes don't specifically say anywhere that the fish immediately turns into a dead fish upon being caught (although it does seem like that's probably how fishing works ). I am holding out hope that the fish stays alive for a while in one's inventory, perhaps dying after a certain amount of time has passed.
We already have the wolf pup you can purchase from traders, which is a live animal you can have in your inventory and can release into the world if you want. It seems like it would be simple to have fish work in a similar way.