Yup, fake it til you make it! Even if you're quaking on the inside, act as if you are confident until you actually become confident. You can do it!!
The only thing I will add is to have a plan before you reach in. I have one snake that occasionally tags me when I go to pick her up. When reaching in for her, I first tell myself "she might bite me, but I KNOW it won't hurt. It is suprising because she's fast, that's all. So if she does bite, I'll just carry on picking her up as if nothing happened." For some reason, having a plan in place just makes me feel calmer, and to be honest, she's never bit on a day when I remembered to do that.