Cicadas don't kill whole trees unless it is a very small tee, the kill branches when they lay their eggs under the bark and that killed the limb or twig, then the limb or twig breaks and falls to the ground and the larva bury in the ground and pupate and then emerge as adults come out of the shell and start the process all over again. They like branches around the diameter of a pencil. The recommended mesh size to use when netting the canopy, you do not have to wrap the trunk, is no larger than one quarter inch. If it were me I would go for netting rather than spray because it is once and done.
When you are up to your butt in alligators, it is hard to remember your intent was to drain the swamp. Stay focused!