You don't actually need to touch the sauce pan.
1 - Fill saucepan with cold water (if you can't then put empty pan on the stove first then use a cup to repeatedly fill the pan 1 cup at a time until full)
2 - Put on stove
3 - Turn on heat
3 - Wait until boil
4 - Puncture egg and put in egg
5 - Start Timer
6 - Extract egg with a table spoon
7 - Put egg straight into cold pan of cold water
8 - De-shell and eat egg
Wait until water is cooled before tipping it away. In no time you are handling the pan, the nearest thing you need to do is putting the egg in and taking it out, both can be done with the assistance of a spoon. It's what i do.