Usually when I add a wash cloth it is a last resort to bringing up the humidity, it will, but don't soak it.
I usually can get my cooler incubator up to 80% humidity when I add a warm damp wash cloth.
I usually don't put an egg on it, unless I have had to help the chick inside of it, because it has gotten shrink wrapped in the egg.
In the case of shrink wrapping, I start zipping the shell myself, and I get a bowl of warm water and a Q-tip, and I dip the Q-tip in the warm water and wet the membrane, but I don't get the chicks beak wet, I don't want to drown the chick.