dtgreene: Dragon Warrior 2 (NES) has the "cold as a cod" line.
Unfortunately, some killing is required to see that line. The twist, however, is that, when you see that line, it's not because you killed something; rather, it's because you were on the receiving end.
The 'no gill' requirement is what makes the request in my original post so slippery.
Fishing simulators, and games with fishing minigames might be okay if there is an option to release the catch without having caused harm to it. However, in many games, upon having caught a fish, it appears in your inventory or fishing log looking stiff as a board (such as in the Yakuza series). I would argue it would be impossible to photograph a live fish in that pose.
Cooking simulators with fish on the menu might be relevant, provided it remains only a menu item, or live aquatic animals in a tank. If there is no way to beat the game without cooking the critters, then it falls foul of the 'no gill' rule.
We could potentially open this up to all games with fish tanks containing live creatures. I suspect there are quite a lot of those.