Before the chicks hatch they absorb the remaining yolk. They can live off of that yolk for over 72 hours. That's why they can be mailed, they can live off of that yolk for a long time.
Sometimes my hatches in an incubator or with a broody hen are over with within 24 hours of the first one hatching. Those are the nice hatches. I've had some hatches stretch out for well over 48 hours, both with broody hens and in an incubator. By the chicks absorbing the yolk the hen can hatch the late ones while the early hatchers wait. So yes, they can wait in the incubator for a long time. I don't take mine out until the hatch is over.
It is possible to shrink-wrap a chick by opening the incubator after it has pipped but before it has zipped. I've done that. It's also possible a chick can shrink-wrap without you opening the incubator if the humidity is fairly low, that's why we raise humidity for lockdown. Shrink-wrap does not happen that often though, it's pretty rare even if you do open the incubator. Some people remove chicks as they dry off and usually don't have problems but people that remove them are often your best source in how to treat a shrink-wrapped chick.
If I have an emergency in the incubator I will open it and take the risk. But I don't do that casually, I have to have what I consider a good reason to take that risk. So don't let that fear paralyze you if you have an issue but realize it is a risk.
There are some tricks to reduce the chance of shrink-wrapping a chick if you do open the incubator. Some people take the incubator into a bathroom and turn on the hot shower to steam it up, raise the humidity in there. I don't go that far. You can put warm (not hot, 99 degrees Fahrenheit is warm enough) water in a spray bottle and mist the unhatched eggs. I don't do that either but is a reasonable approach. I just keep it open as short a time I can and handle the emergency.
Congratulations on your success so far and good luck with the rest of the hatch.
