Go out and fish it’s one of my favorite hobbies, kayak fishing specifically. I prefer to eat saltwater fish except trout. Both my wife and my families have beach places but I’m still limited to 6 or so trips a year.

It’s hard to tell but you could research the types of fish plus the methods it’s caught. Lots of fish need to be bled out so they are incapacitated before bleeding. You can kill a fish instantly by a brain spike (ikejime) or bash to the head with a blunt object. As you said some fish are just thrown on ice but it can depend on the species. Even worse, methods are going to vary wildly from fishermen to fishermen and region to region. Wild caught is probably better than farm raised death wise.