Not really.
Organic is about prevention and proaction, not after thoughts a year after you've had the problem and after the dormant season when the organic spray works.
It depends on how bad the worms are and what they are if organic would be successful.

You've already missed the dormant sprays and orchard hygiene. You could try setting out a lot of traps hoping to thin the herd. Traps would also allow you to better identify the pest rather than "worms".

Spraying pyrethrum and rotenone when the traps show the targets are active may help thin them.
But remember that "organic" does not mean "safe", these are poison to both life and environment if used improperly. They are broad spectrum and don't discriminate between pest and beneficial.
Everything is a chemical organic or not.
They also aren't that effective on fruit pests and it's very much like you're hoping to thin enough to get their numbers to tolerable levels.
You may thin them further by spraying a summer oil.
There may be a BT that is effective on the ground dwelling larve, I don't know.

If the problem is Curculio even a lot of chemical sprays aren't effective. They're the main reason I gave up attempting organic fruit, although Apple Maggot being active most of the season to destroy the rest of the fruit helped me make the decision. I could handle eating around a Codling Moth worm.

A barrier spray like Surround would work before the fruit is big enough to bag, but it washes off in spring rains. Then bagging should keep them off the fruit once it is large enough to bag.

Through the year pick up and destroy fallen fruit, be vigilant (if they're not too damaged eating counts, just don't toss the bug larve into the compost). Clean up debris in the fall. Knock off any loose bark were insects may hide.
On a nice day in late winter/early spring while everything is still dormant spray dormant oil.

Between all that you may thin them down to tolerable levels.

The best organic spray for wormy apples is spinosad. The homeowner can buy it under the Monterey Garden Insect(?) Spray -- look for spinosad listed as the active ingredient. Several places on the Internet sell it if you cannot find it locally. Pheromone disruption lure for codling moth also works well but no places sell just a few of them.

As mykl mentions there is also the plum curculio to worry about; Surround is the product of choice for that.

In general growing apples organically is a significant commitment. If you want to try I would first get Michael Phillips' book The Apple Grower which will give you a basis of information to start from.

Scott

Bitterrooter, where I live may be close to you if Hamilton, Florence, Darby, and Lolo sound familiar. If that's the case you are very near the MSU agri experimental station on Quast Lane between Corvallis and Hamilton. Go there and ask Dr. Callan what is working for growers in your area. Some of them are using pheromone disruption techniques and it's helping. You might also contact the county extention agent in Missoula, and speak with either Sandy or Helen about pheromone disruption. The will be buying a lot of pheromone flavored twist ties and will make them available at cost. This is all assuming, of course, that you're what we in Montana refer to a a Bitterrooter- someone who lives in the Bitterroot Valley.

Other than that I can only second what Myk1 and Scot say. I will add that Spinosad seems to stop codling moth larvae from making a full penetration into an apple and destroying it, but doesn't necessarily prevent it blemishing the apple. That's something of a hassle because it makes it hard to tell whether the apple will be useable. BUT, it keeps that larvae from maturing, so a few seasons of application should make a huge difference. I'm going into my second season with Spinosad and Surround this year, and will add bagging with footies as well. After years of very careful hygiene and spraying and such I hope to be able to claim a substantial crop of "organic" apples. In the past I've used malathion with some success and I've carved codling moth frass out of a fair number of apples too!

Good luck,

M

That Spinosad must've been after I'd given up on organic but before I decided to spray chemicals. Or at least after I'd given up on Organic Gardening Magazine.

I like it other than the part where it harms the beneficial wasps. I think they're the reason I've been so successful in the garden.