i dont have an answer but i think it is related to:
1. all the animals (not on the ark) were destroyed because they and the whole world including the land itself, became corrupted from the corruption of man. the fish ,in some sense, lived in a different world than man and were not influenced by his corruption. the fish were therefore NOT destroyed by the Mabul.
2. fish were always allowed to be eaten. animals were only allowed to be eaten after the Mabul
3. no fish has a trachea, which is one of the two simanim that have to be shechted
4. fish are not brought as Korbonos
what this all has to do with Shechita, i have no idea, i just have a feeling there is a connection