if you have LOTS of flowing water, you may be ok... but something to consider is the Cherokee used to use black-walnut husks to stun/drive fish through their weirs and into nets... It certainly does have an effect. I sympathize with your wishes not to cut down nice trees, they're very good shade trees as well. Your best bet is to get
ALOT of water flowing through that thing and then wait to see how the fish tolerate it. You may get no effects, but most likely you'll just have fish that aren't very happy and won't grow/eat well. If the water flowing through the pond is minimal or non-existent then my guess is they won't survive after the first good fall season...
Depending on the shape of your
berms, you may be able to get away with just trimming the branches overhanging the ponds and let gravity/runoff take care of the rest...
On our farm, sensitive things will absolutely NOT grow within the drip line of a black walnut tree.