You can fabricate a crude form of cellulose acetate which is a form of thermoplastic. It can be created with cotton and other natural fibers and concentrated vinegar aka acetic acid. Both of these substances would be relatively easy to obtain.
If the solenoid can be activated by mechanical means instead of electrical. That is moving the piston by another way to engage the contact. This is also an alternative to avoid having to rebuild the solenoid thereby avoiding the need for copper wire and an insulator. A little bit of creative engineering.