If you can't have anything plugged in, no chameleon is going to work out. Have you considered also the cost of a proper set up? It can cost several hundred pounds for all the proper supplies. Plus, you have to have live bugs in the house because chameleons only eat live insects. Your parents need to be okay with that or it will never work out.
I think there's a lot of reading you should do before getting anything. Here are some good resources to learn about chameleons: