An elliptic curve key, which is what possession of bitcoin is, is just a large number. To send a bitcoin you need to create a "transaction", and in fact the only aspect of generating a bitcoin transaction that requires energy is the SHA calculation, not something you can do in pencil, the EC math is actually simple enough that a computer is not required.

Also your argument that cash does not require energy does not apply to the cashless society we have become today, when was the last time you actually used cash? Credit cards are useless without electricity.