I train slightly differently. Everytime I click, I give a treat. A click is a promise for a treat. I always, always, always give them a treat if they hear a click. When the time is right, you can take away the clicker. I use the clicker when I'm training for a new command. Once the dog has it solid, I stop with the clicker. The clicker is there to help you teach in steps.. but once the steps are done, there's no use for the clicker anymore.

Are you sure she's snapping at your hand because she's afraid? I noticed Kai would nudge my hand or even mouth it when I was introducing the clicker to him. I knew he got it because when he heard the click, he automatically knew a treat was coming.. hence the reason why he went straight for the treat. She could be snapping because she knows a treat is coming, or because she isn't getting a treat and thinks she should (and she should, every single time).