Use Google hangouts instead. It's much better behaved than Skype.
Hangouts . . .
I find them far less controllable than skype. With hangouts, you don't have any choice about letting it skim your contacts list.
At least with Skype you can keep them completely separate.
Skype in the background doesn't hammer battery life much. I'm pretty sure mine doesn't start up automatically anyway (I'm on a nexus).
My daughter has a kindle fire, she took that cycle touring for a week, watched movies on it most nights. It has Skype on it. She didn't have a battery life problem.