A healthy chick can go 72 hours or more from hatch until it needs to eat or drink. The postal regulations on shipping chicks use that 72 hours. The chicks must be shipped within 24 hours of hatch and must have a reasonable chance of delivery within 48 hours of shipping, a total of 72 hours. So you have more time than you thought.
The risk of opening the incubator when an egg has pipped is that you could cause an egg to shrink-wrap. That's where the membrane inside the egg dries out and shrinks around the chick so it can't move or hatch. By opening the incubator you allow moisture to escape. If a chick has pipped the membrane is in danger of drying out. There are threads on here that tell you how to assist in the hatch if a chick is shrink-wrapped, it would not hurt you to look for one and read up on it just in case. As much as some people on this forum seem to be in denial it can and does happen.
But it does not happen that often. It really doesn't. Since it can happen I consider it good practice to not open the incubator after lockdown. But since I know the risk is low, if I have an emergency I will open the incubator and take care of the emergency. I did shrink-wrap a chick doing that one time so I am convinced it can possibly happen, but a lot of other eggs did not shrink-wrap. I consider the risk fairly low but why take a risk with a chick's life if you don't have to.
Sometimes if people are going to open the incubator they steam up a bathroom to raise the humidity and open the incubator in there. It is less likely to dry out. Some people put warm water (around 100 degrees F) in a spray bottle and gently mist the eggs to keep them from drying out as much. Just gently mist, you don't want to soak the egg or drown the chick if its beak is sticking out. I don't do either of those things and it is still seldom a problem. I've done it a few times, just not as a habit.
For what it's worth I once had a hen hatch a chick late on a Monday. About 80 hours later she brought her chicks off of the nest to get food and water. The chick that hatched first was fine after all that time.
Practically all of my hatches are over with within much less than 48 hours, some as quick as 16 hours and most are about 20 chicks, but you never know when one will stretch out. I think it is a good question.