There are other dangers than pesticides to be concerned about as well and you should clean fresh produce, organic or not, better than how you'd clean it for your own family. Pesticides on the skin can be successfully removed, as well as other bacteria.
You can try using products like Avicine (a bird safe disinfectant) or GSE to clean the produce. Do not use any other chemicals to clean the food, just use clean water and thoroughly rub and scrub the entire surface of the food. Do not wash produce until you're going to use it to prevent introduction of microorganisms. Store fresh produce in the fridge in cloth bags or perforated plastic bags to allow air circulation. Peeling is an effective removal of bacteria or pesticides but do be sure to rinse to prevent cross-contamination.
Finally, don't worry yourself to death...that's a good way to end up in a padded room, with your stressed out and likely plucked naked parrot in the padded room next to you! You can only do so much to prevent accident and illness in your bird...or in your family for that matter. Use your best common sense and continue to seek out advice when you're not sure. It's clear that you are a responsible, caring pet owner and I'm sure your parrot will thrive!