Cook in oil, add the flavoring sauces later on. Veggie oil ought to be fine. Olive oil has too low a smoke point, and will add flavors you don't intend. Don't use too much. Tablespoon or so.
You don't have to boil the shrimp before shelling them. What I'd do is, peel the shrimp raw, heat up a little oil (but don't let it smoke), toss the shrimp in there, and stir-fry them until the shrimp are more or less cooked. Then add the tougher veggies (zucchini, peppers, etc) and whatever aromatics you're using (onions, garlic, etc). Finish up with the more fragile veggies or the things you don't want wilted too badly (sprouts, herbs, etc). I'd serve just like that, with sauces on the side.
You'll be fine doing this in a frying pan. If you get into making this sort of dish, you'll want a wok before long, but it can totally be done in a flat pan.
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