Bringing preserved insects and arachnids on an airplane

As carry on or checked in luggage, or shipped? Shipping is your best bet by far. The shipper will tell you what you can and cannot ship and how it needs to be packed.
In luggage, you have two approvals to go through; security before leaving and approval upon arrival and they may have very different standards. A checked in bag can get flagged for all sorts of reasons. Finally, carry on is usually limited with liquids to properly labeled containers of 100 ml or less and security can arbitrarily confiscate anything that they choose.

I've spent way too many hours/days cooling my jets trying to get something passed through a port of entry. Life is too short! Ship the dang thing!