I make zucchini bread at least twice a month during the summer. All I do to the zucchini is wash it off and the cut the stem off. I then grate it by hand using the larger holed grater. I do not peel it. I like the bigger shreds of zucchini because it makes less zucchini juice mess that I have to drain off.
Just wash the zucchini, cut the stem off, and grate. It's a lot less waste if you don't peel it. Sometimes if it is a bigger zucchini, I cut it in half and take some of the seeds out as they won't shred in a processor.