Interview with Heirloom Squash farmer:
First, putting non-host species between squash plants may help. Squash bug nymphs must go through several stages of molting before they become mature; the nymphs feed as the adults do, but can’t yet fly to explore what else you’ve got for them to wreck.
Next, exercise constant vigilance. Check plants at least weekly for egg masses and crush them when they appear. Crush any adults you see.
Keep mulch away from the base of the plants; get as much air and light around there as you can. Deny them a hiding place.
Finally, diatomaceous earth around the base of squash plants can help; it’s benign enough to be permitted in certified organic cultivations.
“The key is to get the first generation when they’re small — the first half of June,” Cranshaw says. “Nail ’em then. Get ’em before they breed. If you do a good job then, you’ll keep their numbers down.”
Vadas-Arendt has a trick she uses to thwart a cutworm that attacks squash seedlings:
“Plant a little, 3-inch-long stick right next to each little stem.” The stick prevents the worm from encircling the seedling.
To help thwart the powdery mildew that often besets squash leaves in the late season, she uses a spray made of 1/2 teaspoon baking soda, 1/2 teaspoon mild dish or hand soap, about 2 teaspoons of milk, shaken in two cups of water. “You can get an extra three weeks out of your plants this way.” Denver post

Organic
And a side note, if you’re worried about pesticides in your food, be wary of buying conventionally grown or any non-certified organic squash or cucumbers. The cucurbit family is notorious for up-taking the chemicals in the soil, that may be there from years past. Even if the grower does not spray and uses organic methods, chemicals that have not been allowed in farming for decades still persist in many soils and many organic growers have to have squash tested at harvest time to determine if it can be sold as organic or not. - Growing Naked Seed Pumpkin

Note: some use chrysanthemum oil.