Before they hatch, chicks absorb the yolk. They can live off of that for about three days or even more for both food and water. That's why they can be shipped in the mail. You don't need to take them out immediately. You can easily wait two to three days.
You'll get a lot of dire warnings about shrink-wrapping chicks if you open the incubator during the hatch. There is some risk involved if you open the incubator and an egg has pipped but not finished hatching. The chick is surrounded by a membrane that can shrink around the chick and prevent it from hatching if that membrane dries out. When you open the incubator, you release some humidity that is in there. If the egg is on the verge of becoming shrink-wrapped that may be enough to send it over the edge. If an egg has not pipped the risk from opening the incubator is pretty negligible, but if the egg has pipped, it is possible.
I've shrink-wrapped a chick before by opening the incubator so I'm convinced it's possible. But I have also not shrink-wrapped several chicks that had pipped when I opened the incubator. I understand there is a risk but sometimes you need to do something in there. I'll open the incubator during hatch to take care of an emergency, but I consider it good practice to not open the incubator without a really good reason.