Been there...done that. DS egg allergy is not life threatening, but the peanut one is. WDW is wonderful at keeping people safe.
Planes- Try to book the first flight of the day, less chance that someone was eating peanuts before you get on the plane. You can call and request that peanuts not be served on the flight and they can request that no one eat peanuts on the flight but can not forbid them doing so. One idea that seems to work well is to carry a nice selection of peanut safe snacks and offer one to anyone sitting close to you that has an unsafe snack. Some suggest having regular M&Ms. While they are not safe for your child, it is safer for someone to eat those near your child than the popular peanut M&M's that often are offered on planes. Take plenty of epi-pens (our doctor recommends one for every 15 minutes of flight time), and try to pre-board to wipe down seats.
WDW food- They are very good. Note it on your ADRs and mention it as soon as you are seated. A chief will come to the table and talk with you. All will make it safe, some will make it special. Desserts are pretty limited. You might want to bring some sweet treats with you. At CS, ask to speak to a manager and to see the ingredients list. Understand it will take a bit longer to get your food. Do your research and understand the labeling policy on some of the products. For example the Micky Bars are made by I think it is Nestle. Some people are ok with them being safe, others are not. Ask lots of questions and be very clear on what your needs are.
Resort room- Ask for a special cleaning and still inspect the room really well...we found an m&m under the bed once

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Wiping down ride- We do not....really not practical or possible. Rides load fast. Just wash hands often and try to keep them out of his mouth. Be alert at all times. We have had to get out of line when someone in line was eating peanut butter crackers

. We do wipe down benches because a lot of people do sit there to eat, and of course tables. The disposable place mats are a must have.
Try to relax and have a great trip!