Just take one half at a time; break a piece of egg at the rim and remove it to expose the membrane edge to grab.
Carefully peel it to the bottom (so as not to tear) at a 30 degree angle or so from the inside of the shell-side.
The more surface are you have a hold/leverage on with the fingers, the less concentrated pressure and lower likelyhood of tearing.
You know how you can peel an orange in one piece? It is that same idea just work the piece bigger; loose at each edge and down and it will tear sometimes that's okay: It is like a zen practice or something haha.
The main thing is to prevent breaking the eggshell into small pieces because then it really can become a pita
Also; are you using fresh eggs? That might be easier; maybe soak them for a minute to rehydrate before mostly drying and continuing if they aren't fresh shells?
Maybe a simple wet washcloth covering a finger would work to wipe it away.
Maybe a journey to the health store for pure CaCO3 (Calcium carbonate) antacid, or shopping for sufectant-free (often called "clear"
ammonia (do an evaporation test) would be better options for snorting or smoking; respectively.
Blessings.
All readable matter in the above post is ficticious.
Any similarities to real life are purely coincidental.
Without prejudice.