Hello. Thank you for coming to JustAnswer with your question, and welcome.
Pre-washing vegetables does not affect the nutrient value unless they are then put away and stored wet, which might lend to faster spoilage. Also, it depends on the type of vegetable---broccoli and cauliflower are sturdy enough to handle being washed ahead of time. (unlike spinach or lettuce for instance).
Wash the vegetables, as you have described, and let them dry thoroughly before packaging and putting them in the refrigerator. They will be fine, and just as nourishing as they would be if you waited to wash at the last minute.
I recently read about some research that has been done about the loss of nutrients in food with aging. The researchers found that, not only did most produce not lose nutrients, some actually had more with aging. I know this has nothing to do with washing, but I thought you would like to know--so there's nothing wrong with using produce that is about to wilt, though better used for soups and such. And personally, I will wash some vegetables and let them air dry before storing as soon as I get home from the market. It will not affect the nutrients contained, unless (like I mentioned) the washing would actually damage fragile leaves and such.