I think it's not the letting them out that stresses them so much as the process of putting them back in! Which stresses out EVERYONE involved.
One shortcut I tried and got lucky with to get a chin used to you/ not terrified of you: Open cage door. Lie in front of cage door. Sprinkle apple sticks and rose hips on your tummy. Take a nap/ read a book/ etc.
With any luck, chins being naturally curious and inquisitive creatures, they'll eventually investigate and come eat the snacks. Eventually labelling you in the "harmless" category.
Oh yeah... that's a major difference between chins and dogs/cats/etc.... you don't go straight from strangers to friends, you go from "potentially dangerous" to "non dangerous" to "I don't mind this person" to "friends"
Whatever you do, make sure not to slide from "potentially dangerous" into "confirmed dangerous" labelling, as chins apparently never forgive such things, or so I've heard.
Oh, also, taking a nap is a two edged sword in the above scenario... probably safer to stay awake, but it could take AGES for a new chin to pluck up the courage to climb on you and take the treats...