Permethrins and especially pyrethrins are generally very safe. They both are components of flea and tick applications for dogs and cats. I would use the spray on your vegetables-I do. As always, thoroughly wash all of your vegetables before eating.

Only as a last resort!!

Because it is a nerve toxin, it can kill some beneficials such as lady beetles, so use only when necessary to control a particularly bad outbreak of aphids, bean beetles, stink bugs, potato beetles, celery leaf tiers, cabbage loopers, mealy bugs, red spider mites, whiteflies, thrips and more.

Instead,
Go to your local garden center/nursery or Lowes/Home Depot and buy Safer's insecticidal soap (Safer's is the brand name) and spray on the aphids. Also, look for ants on the ground around the infected plants, they like to terrafarm the aphids, you may seem them transporting the eggs. If so then you should spray them as well.

Coffee grounds if not composted can also kill beneficials so do not sprinkle around, its does wonders when added to compost though.

Here is a link that might be useful: my veggie blog