Soak bean threads or rice sticks in hot water until soft, about 30 minutes. Drain thoroughly and cut into 4-inch lengths.
Snap off stems of snowpeas and discard. Blanch snowpeas for 5 seconds in in 2 quarts boiling water. Immediately transfer snowpeas to a bowl of ice water. When cold, drain and pat dry, then cut into fine slivers. Stem and seed pepper, then slice into 2-inch slivers. Remove and discard dirty ends of mushrooms and separate strands.
In a food processor or blender, mince the garlic and ginger. Add orange peel, cilantro and green onions. Process until finely minced, then add remaining dressing ingredients and blend to combine.
To assemble, combine the bean threads (or rice sticks) with the other salad ingredients. Pour the dressing over and toss to combine thoroughly. May be prepared up to 2 hours in advance.