have you ever heard of a product called "pink solution"? it's an all-natural enzymatic-action coconut-tallow blahblahblah all-purpose cleaner, but it says right in their "other suggested uses" that you can use it as aphid control too. i've actually purged the upstairs of chemical cleaners in favour of it, part of the sales pitch is that it's completely safe and the salesbitch sprays the light solution right in their mouth. (<-sold me, as a soon-to-be mom lol) i've only ever seen it at costco and trade show kiosks, otherwise you have to order it directly from them, i think.
idk if they distribute to the states, but while i was researching it i read that there's an american company with a similar product (i forget what they're called now). (whenever i encounter a too-good-to-be-true product i google the company name with "scam" tagged on the end to see what it comes up with.)
anyway, just for shits and giggles i tried spraying a branch of my infested mock orange with it last year and it worked. for about 5 days, that branch stayed aphid-free.
it's one of those products that has quickly become part of my "new parent" arsenal, figured i'd share since you're going to be a fellow aphid-fighting parent soon