no, I have heard that if you don't wash they can be placed on the counter for a couple of days insted of in the frig. I was the poop off mine all the time and have had no problems.

This is the method that I use and prefer, to prevent contamination. Your water should always be warmer than the temp of the egg to prevent the warmth of the egg from drawing contamination in through the shell:

"If eggs require cleaning, they can be brushed off with sand-paper or washed. If washing, a water temperature at least 12 °C higher than the eggs themselves should be used. A sanitizer should also be used in the water (not dishwashing liquid). Water with a high iron content should not be used. Eggs should be rinsed and then completely dried prior to storage." From farminfo.org

Are you able to improve the chicken area so they aren't in mud? I am working on doing that too, adding a clear roof over 3/4's of the pen with wire over the the other 1/4, so it doesn't get muddy this year.

And here are some good books that might be helpful:

A Guide to Raising Chickens : Care, Feeding, Facilities (Storey Animal Handbook)
by Gail Damerow - Publication Date: January, 1996

The Chicken Health Handbook - by Gail Damerow - Publication Date: June, 1994

Small-Scale Poultry Keeping : A Guide to Free Range Poultry Production - by Ray Feltwell - Publication Date: October 1992

Best to you,
Michele