The rechargeable part will not be the fan but a rechargeable energy storage. The energy from the storgae will be used to power the fan. You'll need a means to recharge the energy storage and to discharge it to power the fan.
Make a list of the parts required and how to interconnect them, as Bob suggested. We'll be happy to check your results.
Just a note on the side, but please don't get distracted: while you're probably looking for electric and electronic parts to fulfill that purpose and that is probably in the way of the answer your instructor is expecting, there are other ways imaginable that work on mechanical principles.