You don't need to peel the zucchini before you use it, since it will cook through in the oven.  Just use the biggest hole cheese grater that you have to grate the zucchini.  If you try using a small one, the zucchini may dissolve into mush and water.  To remove some of the water, I placed the zucchini on top of three stacked paper towels.  Then I just folded in the corners and lightly squeezed.  The zucchini shreds should still feel wet when you throw them into the batter, but they shouldn't be dripping.