It all comes down to how much moisture the vegetables have in them. Shredded carrots generally aren't that wet and can be added without adjusting the recipe. Zucchini on the other hand is notoriously moist and shouldn't just be added to a recipe that isn't calling for it without significant changes in reducing moisture elsewhere in the cake. 

As for substituting applesauce, since it does not have any fat in it substituting it for butter or oil will give you a much less rich tasting cake. 

Happy baking!

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