Whiteflies are actually tiny moths. True whiteflies create sticky nests in which they lay their eggs. There are also damaging pests that lay their eggs in the soil but otherwise look just like white flies when they are flying around.
The gestation cycle is very short, so repeated treatment is usually needed at short intervals, typically 3 days. For bad infestations, four treatments is usually sufficient.
True whiteflies will be killed on contact with a pyrethrin, which I consider very safe. Most fruits and vegetables at supermarkets are sprayed with a pyrethrin almost daily.
If you have the pseudo whiteflies you'll have to use something stronger (sorry). Those buggers are resistant to pyrethrins, sevin, etc. Malathion will work -- or most chemicals that work on thrips.
To decide whether a particular chemical meets your safety criteria, look it up at
PAN Pesticide Database