I've only had a problem with shipped chicks a couple of times, right after they arrived. I just keep an eye on them and clean them as needed. After a couple of days, it usually resolves. For mine it did. I just keep them warm enough, out of drafts, keep their brooder/paper towels clean, keep their water clean, keep them on chick starter and make sure they are all eating and drinking.
I try to get chicks when the weather is not too cold or too hot, but it's still stressful for them. Think of everything they went through at the hatchery and to get to you, including the fluctuating temperatures. Some shipments have a rougher trip, some have an easier trip. Plus, everything is new, everything is scary and their little digestive systems have never had food before. Sometimes, it just takes a couple of days for everything to work right.
For a really bad case, I had one chick that I cleaned under the faucet of the laundry tub. She was really caked, with a large amount. I don't know how she managed that over night! I made sure the water was a comfortable temperature on the inside of my wrist and rechecked it occasionally while I was working on her. Only her backside got wet and I think it was easier on her skin. The running water was only a gentle stream, but really saturated the blockage well and some of it was washed away, even without the picking. She wasn't red or sore afterwards. I blotted her dry when I was finished and put her back with the others.