I am not a peeler. It’s the rare occasion that I take the outer skin off a veggie, even with non-organic items. You can’t peel the pesticides off and why lose those surface nutrients and fiber? The exception is obviously waxed vegetables. That can lead to an awful aftertaste in the food you cook, so peel those, please.
To dice (or for any veg prep), wash the vegetable and wet your cutting board with a sponge or a wet cloth. Wetting the board prevents nutrients from the cut veggies from absorbing into the wood.