Eggs can be stored at room temp. Except in extreme situations i don’t think i would use mineral oil, but an oil more meant for consumption, like olive oil. The mineral oil will penetrate the shell into the egg to some extent.
Olive oil turns rancid at room temperature
I recommend PB Blaster Penetrating Catalyst Oil - it builds strong bodies twelve ways...!
When I was sailing offshore, I used to coat my eggs with wax. Just make sure that the eggs have never been refrigerated then dip them in hot wax for a moment.
I’m not sure why the eggs should be fresh, never refrigerated; that’s just what the old salt I learned this from told me, and I never had reason to try refrigerated eggs.