unshelled would be shorter.Goodness, I should think a week a bit too long. I would say if properly covered etc., they should be fine until the next day but no longer.
in the Uk your fridge is probably warmer than outsideWell, I boiled 3 eggs on Saturday, shelled them and refrigerated them overnight, took them on a 20 km hike on Sunday (ate one), put the remaining two back in the fridge, then ate them today (Wednesday) and they were fine.![]()