There are organic solutions for this, though it might be too late this year. See the pest control solution chart at http://www.groworganic.com, or speak with the folks at http://www.treesofantiquity.com/ or http://www.ediblelandscaping.com/ Both of those companies grow fruit trees organically. I don't know what kind of worms they are (apple maggots? I believe there are good lures/traps for these), so I don't know what to tell you exactly, but they should have good details on their sites.
Oh, another organic apple growing site: http://www.herbsandapples.com/orchard/ This guy has a book about growing apples organically; maybe you could find it at a local library. Good luck to you.
I haven't had apple trees in years but I recall making a coddling moth lure out of milk containers, mixing molasses and apple cider vinegar with water. It worked well to lure the moths and they drowned instead of laying eggs on the apples. We got plenty of apples. The worms are apparently the larvae of the coddling moth.