1. Soak eight 8-inch wooden skewers in water 15 minutes. In a food processor, pulse cashews with curry paste and 3/4 cup water until smooth. Combine 1 cup of cashew mixture with 1/3 cup water. Toss chicken with remaining mixture; lightly season with salt. Meanwhile, bring a large pot of water to a boil. Cook noodles until just tender, about 2 minutes; drain. Rinse with cold water; drain well.

2. With a vegetable peeler or mandoline, shave cucumber and carrots into wide, paper-thin ribbons. Heat a grill or grill pan to medium-high; lightly brush with oil. Thread chicken onto skewers; grill, in batches if needed, 6 to 8 minutes per side, transferring to a plate as done. Serve, with noodles, lettuce, cucumber, carrots, cashew sauce, chopped cashews, and lime wedges.