The mercury content found in fish is from environmental exposure. It's a cumulative bio-toxin, meaning that as they ingest mercury it never really gets excreted out much, but continues to build up. It's generally not an issue except for relatively top end predatory fish. The prey fish on the low end of the chain get very low exposure, but the predators above them get exposed to the whatever their prey was exposed to. So that predator, which might be 2-10x the size of the prey, gets the same exposure as the cumulative amount as the hundreds or thousands of prey fish it eats saw. And the next one up the chain, and so on, until a human catches it and eats it.
For fish you are raising that is not much of an issue. In that case the only way to keep them from building up mercury would be to ensure that their food was free of mercury (no idea how you do that). But they can also get some exposure from dust borne mercury. Nothing much you can really do about that, other than keeping the fish in a closed system that prevents outside dust from getting in. Which would be very difficult and costly.
Best bet is to cut the fish to minimize the amount of mercury you ingest from them.
Most of the mercury will be found in the belly fat. So if you trim that away you eliminate the largest source of possible mercury contamination. Sorry - that's PCB's that are in the fat. Mercury is in the muscle.
https://www.doh.wa.gov/Portals/1/Documents/Pubs/334-098.pdf