You don’t need to dry them before removing the stocking. Just wait for them to cool or run cold water into the pot.
The eggs are still pretty strong. If you are carefull with them and store them in an egg carton between Easters then you can keep them forever without breaking. My mum has a huge collection of dyed and painted eggs. She displays some in a bowl, some in egg cups and some hanging.
To hang the eggs, tie a piece of ribbon or thread around a piece of toothpick and insert it into one of the holes. I used scissors to score the toothpick in the middle so that the ribbon didn’t slip off.