What you are talking about is a cousin of the stink bug called the squash bug. If you look for photos of it I’m sure you’ll agree this is it. They do stink when squished.
I’ve tried every organic method I can find to control it. None have been successful. You can slow them down some by daily searching the leaves and stems for the eggs and crushing those, but eventually they always get the better of me. You can put a board down for them to hide under and get some that way, but that is only some. They breed so fast that once they get a toehold they take over, at least here.
One of the problems is that they do not eat the squash plants, they suck the juices out of the plant. That means if you do use a poison, organic or not, you can’t use one that they have to eat. They won’t eat it. You have to use a contact poison and frankly I don’t know of any organic ones of those. They hide so well that I can’t keep them under control even with non-organic contact sprays either.
To make it even worse, it’s not just them multiplying to large numbers and sucking the juices out, which will kill the plants, but they also spread a wilting disease that can kill the plant. “Little nightmares” is a gentle way to describe those things.
If you are talking about summer squash you might try growing Tromboncini squash. It is a vining plant and needs a trellis but it is not as susceptible to those things. It does take up a lot of room but just one squash goes a long way. The squash bugs will still attack it so you do need to keep after them, but mine Tromboncini lasts a lot longer than zucchini or yellow squash.