If you like your vegetables crisp they can go on the stick raw. If you like them "cooked", meaning soft, you will want to blanch them before putting them on the stick.
Many people prefer to blanch their onions and bell peppers but use the zucchini and mushrooms raw.
Mix and match it is up to you.
It is fun to play! How about a root vegetable skewer? Peel, cut and blanch carrots, turnips, parsnip and celery root. Put it on a stick with onion and bell pepper. Mushrooms are great over an open flame. Mix Portobello, crimini and white mushrooms and put them on a stick with blanched whole shallots. Cook it plain or marinate it in Balsamic vinaigrette. A popular combination is bell pepper, onion, yellow squash, mushrooms and cherry tomatoes marinated in Italian salad dressing. Fennel is an often forgotten vegetable. It goes well on a stick. Blanched asparagus and onion with cherry tomatoes is a nice combination.