I see this battle as a challenge and I keep score! I'll walk my rows of squash and hand pick these pests. You can put them into a jar of soapy water to kill them or do as I do and simply pinch their little heads. If you pinch their heads without squeezing the body you won't be overcome by the odor that qualifies these bugs as true stink bugs. I give myself a point for every squash bug I kill, I give myself 3 points if I catch and kill 2 stink bugs caught in flagrante delicto. On one sunny day I scored about 200 points but most days are single digits.
You'll see squash bug eggs mostly on the top of the leaves of your zucchini. Gently rub the eggs off the leaf, once the eggs fall to the ground there are many predators that will eat them. As much as we hate fire ants, I've watched fire ants craw up the leaf and harvest squash bug eggs. If you find lots of squash bug nymphs, the commercial insecticidal soaps will kill them but it requires multiple applications.
By mid summer the squash bug numbers will be too great and our squash will be overrun with these pests. So we'll outsmart these critters. If we take a break and let our squash plants die so that there is no host plants for the squash bugs their numbers will crash. Then about the first of September we'll plant a late crop of squash which will give us a small crop going into the fall.
So join me in hand picking squash bugs, feel free to pick them from neighboring plots... keep score and we'll see who can get the highest score.