I suspect that the minimum set of fish that will produce all 441 possible species in one generation is more than will fit in a game.

But I think adding Hornets and Arrowfish will reduce the number of generations needed.

After that I would add Finless, Wasps, Quicksilvers and Goldsharks.

I think that will reduce the number of generations needed to 2. If I did the chart right, adding in Speckled, Canary, Leaffish, and Fire-arrows is all that remains to be needed.

So that is:

fins:
Silky
Twinfin
Greenfin
Hornet
Finless
Wasp
Speckled
Canary

bodies:
Shark
Spotanus
Beta
Arrowfish
Quicksilver
Goldshark
Leaffish
Fire-Arrow

if you make all combinations of these, that produces 64 fish. There is probably some redundancy, but I haven't worked out which combos can be removed.

HTH.