Well that was interesting...... a world tour of egg cleaning .... includes washing in bleach in some countries (ugh!)
seems both are better unwashed (no surprise there!)
Hen eggs.....
Quote.....
Wet cleaning
Naturally, the egg has good defenses to help protect the embryo during incubation. The shell is covered by a waxy layer (the cuticle) that helps prevent microbes from entering the pores that allow the passage of gases. The cuticle is not impenetrable and water on the surface of the egg shell can undermine these defenses because water helps bacteria pass through the shell pores into the egg. If the period of contact between egg and water is short, there will be little microbial penetration into the egg (Zeidler, 2002). Therefore, it is important to limit the amount of time that the shell is wet. Soaking eggs in water for as little as one to three minutes can allow microbes to penetrate the shell (Zeidler, 2002).
Duck eggs
similar but as HesterF says water should be warmer than blood temp .....