What do you call the skin shed by an insect or worm? I am sure there's a word for it, and also is there another verb that means "shed a skin"? Because "shed a skin" is a verb and I am wondering if there's a word replacement for it.
Worms don't shed their skin. Snakes do, but you'd call the shed skin a "snake skin". Generally there is no special word, you just say "'animal name' skin" or "... shell" (depending on how hard it is)
Most insects don't shed their skins as adults. Some do shed a skin as they transform from larvae to adult insects. For example, cicada will leave "cicada shells" on trees. You occasionally find grasshopper shells too. You also find shed crab shells and the shed skins of spiders.
The verb is usually "shed" but you can also "moult" and "slough" (as per comment) (Moult also means replacing hair or feathers)
There is a highly technical word, but don't use it unless you are writing a scientific paper. I didn't know this word before researching this answer.
The technical word is exuvia (plural exuviae)
An old word that used to be used was "husk". The OED has this as an obsolete word for "The coriaceous wing-case of an insect; an elytron", or an archaic word for "The shell or case of a chrysalis; a cocoon." that could be left behind.
Not a modern or technically correct word, but it would be valid as a poetic alternative.
: to shed hair, feathers, shell, horns, or an outer layer periodically
// Birds molt once or twice a year.
transitive verb : to cast off (an outer covering) periodically specifically : to throw off (the old cuticle (see CUTICLE sense 1)) —used of arthropods
// a spider, like a lobster, molts its covering as it grows
— Eugene Kinkead
: the act or process of molting
specifically : ECDYSIS
The word is "Exuviae"