I had some aphids on my chili bush once, next thing an assassin bug must have laid some eggs near them. Before long, the eggs hatched & all these baby assassin bugs had a field day on the aphids. That kind of took care of the aphids.
There is also a parasitoid wasp that specializes in aphids.
I wonder if you just leave the aphids, if something in nature will control them biologically for you.