I take care of a couple of properties where beavers are a problem. One consists of a spring fed stream. The other is a small lake of a few acres. I tried traps and didn't like traps because of by-catch. I tried trapping under water, at dam breaks, etc. Under water was the best case scenario, but still caught a snapping turtle (not dead, had to shoot it) and a raccoon. The raccoon was surprise. So I shoot them using thermal.
The problem with shooting beaver out in the water is that they tend to sink. It may take a while for them to float back up, assuming they don't get entangled in the vegetation growing under the water. If you can shoot them on the bank or at the dam, it is better. Of course, anytime shooting around water, be wary that bullets can skip and so make sure there are no down range issues and preferably have high banks as backstops.