Why are we still using all those styrofoam trays for our fish and meat! It lasts forever, and is nasty.
Short of going hunting yourself, or receiving the spoils of another’s hunt, or butchering your own farm animals, the next best stop is the fish monger or local butcher. This is because you can talk directly to the person serving and get them to put the meat into containers you’ve bought for the purpose. Just get them to tare weight first prior to filling.
It is our experience that it very much depends on who you get at either the fish or meat counter in supermarkets as to whether they will agree to avoid plastic and wrap the meat in paper only.
What does your fish usually come wrapped in from the supermarket deli? A plain old plastic bag is less of a problem than a foil/plastic/paper bag. One supermarket chain in New Zealand has these and they look kind of great, like its paper, but it a mush, like a tetrapak, very hard to do anything with.
If they put it in plastic first and then wrap it in paper, it might be appropriate to ask for just the paper.
Or go vego.