Hello Sophie &
Everybody loves peppers, that also includes a litany of insects, not so much with zucchini. Here I make it my mission to know my enemy and they would undoubtedly be aphids and squash beetles, but please understand that that would be the culprit here, I'd be reluctant to say that's what it is there as I have no idea about your area and if there is anything unique to it.
In any case I really don't think you could go wrong with some Neem Oil, it is not unnatural as you may fear, it's organic in nature, but constant or daily application will be required if it is aphids. As to the zucchini check under the leaves for roe or little tiny brownish clumps, if they're present then hit them as well with your spray -- this will have to be done on a as needed basis -- just keep checking under your plants and if you see some gross clusters of fairly good sized beetles, then it will have to be sprayed again.
Another way to control aphids without chemicals is ( lord I hope I spell this right! ) Diatomaceous Earth, there's a lot of theories on it's effectiveness, but I think it just annoys the h@#% out of them. Try it!
Good luck & Good gardening