I too have chemical sensitivities so I can appreciate what your wife goes through. Here's some home made sprays you can make for insect pests and diseases.
You can also use IPM - Integrated Pest Management strategies. That could be a biological control like attracting a good bug to be a predator of the bad bug or another organic control. It helps to know which pest is the problem. With your apples I suspect the problem is the apple maggot though there are other pests that leave worms in apples. Many people hang red sticky balls in their trees and the maggot fly is attracted to these and get stuck.
Do you know which pest it was?
Here's a site about growing apples without pesticides.
Here's a bunch more ecogardening factsheets.
This site is from UC Davis in California but has lots of helpful info on IPM
Here's their page for crops. If you click on 'Apple' you might be able to determine which pest it is and find helpful info too.