When it is fresh is probably the best time to do it. The longer they sit out, the more they dry and the more likely they are to be damaged accidentally. I suspect that you could drop the molt into hot water and it would soften up enough to spread out (like we do with dried insects). Sometimes I've placed a piece of paper towel above the specimen to hold it under water in a container. Many people will put pins right through the specimen, however the pins can be placed into the pinning board (or a piece of Styrofoam, etc.) at an angle so that they simply hold down the specimen, rather than puncturing through it. It takes more pins to do it this way, generally, but it helps to preserve the specimen. Once it is spread into a final position, allow it to dry for a week or two. Something as thin as a molt would probably dry sufficiently in a couple days. Many people buy cheap "Riker mounts" to hold their specimens, but there are endless options. Whatever you use, the specimen must be completely dry, to prevent mold, and the display case should be air tight to prevent entrance of dermestid beetles and other scavenging pests.