Here is a little trick I learned while working in the food industry to speed up the process to remove egg shell from a hard boiled egg.
I am wearing nail polish in these photos (sorry), as I am only preparing these for myself. If you are working with food to feed people outside of your family and/or close friends it is best to not wear any nail polish. No one working in the food services should be wearing nail polish, as this can be a health issue.
There is an air bubble inside the shell at the bottom of your egg. Smack the egg down onto the surface to break the shell. Your egg should be able to stand on it's own like that.