Fishing is strange and unintuitive, and doesn't work like you think it does.
Vermin fish - the small creatures you see appearing and disappearing in your river - can move by teleportation. They appear and disappear randomly in any body of water that is of the right biome for them to be found in. They do not actually need to be capable of physically reaching a body of water in order to appear in it. River fish will sometimes appear in isolated murky pools near the river, despite there being no way for them to have reached them. It is therefore irrelevant how you're moving your water into your isolated fishing area - river fish may appear in it anyway.
However, just because you can see vermin-type fish creatures moving in a body of water, doesn't mean you can catch them. Each biome has an invisible population counter for all creatures that may appear in that biome. When you designate an area as a fishing zone, the game checks the biome that zone is located in to see if it has fish. It does not matter where the water in that fishing zone came from, or if there are vermin fish swimming around in the water. If you dig a fishing pond underground inside your fortress, the game will look at the underground biome population to see if you can fish there, even if you pump river water into your fishing pond. Furthermore, when a dwarf performs the fishing task, what kind of "fish" he catches is determined by the biome population and not what kind of actual fish may be swimming around, so a dwarf fishing from an artificial indoor pond is at best going to catch turtles, even if the river is full of fish.
To have your fisherdwarves catch fish, they need to fish directly from the river, or from an artificial pond that's close enough to the river to be counted as part of the river biome.
My advice would be to catch or kill the gators, they're more worthwhile than the fish anyway.