This answer to the question How to clean and preserve a cicada's molted exoskeleton (exuvia)? states:
The exuvia is made of cross-liked chitin, and will not decay. You don't need any special preservatives as all. If you need to get the mud off, just rinse it as you said, in soapy water, let it dry, and you are done. Simple.
Wikipedia's Chitin says only:
Chitin is a modified polysaccharide that contains nitrogen; it is synthesized from units of N-acetyl-D-glucosamine (to be precise, 2-(acetylamino)-2-deoxy-D-glucose). These units form covalent β-(1→4)-linkages (like the linkages between glucose units forming cellulose). Therefore, chitin may be described as cellulose with one hydroxyl group on each monomer replaced with an acetyl amine group. This allows for increased hydrogen bonding between adjacent polymers, giving the chitin-polymer matrix increased strength.
I'm not a chemist, but "increased hydrogen bonding between adjacent polymers" doesn't sound the same as cross-linked polymers. So I would like to ask for an answer based on sources other than Wikipedia:
Question: Is the chitin in an insect's exoskeleton cross-linked? If it depends on the type of insect, then the focus should be on "a cicada's molted exoskeleton (exuvia)" as discussed in the linked answer.