Congrats on the egg! My husband washes a lot more eggs than I do and whenever I give eggs to a friend always makes a comment asking if I washed the eggs in front of the friend. I just want to smack him or tape his mouth shut. I pretty much only ever wash duck eggs because they often have mud caked on them. Even then, I don't wash it until right before I crack it in the pan. That is a good compromise actually. Perhaps your husband can be convinced that if you wash them it should be right before you cook them, also to crack them in a separate bowl first instead of right in the pan just in case you get a bad egg. I'm not that worried and don't always do these things, but they are things my husband can do to make him feel safer about eating them. Also I make sure I keep them rotated so that I'm eating the oldest eggs first and don't end up with any sitting for too long.
Congrats on your egg!!! This thread has good info for him, and links to more information! I finally got my husband on board with not storing in the fridge, I date them in pencil to help keep track of how long we've had them.