For Ginger Slaw, toss together cabbage, bell peppers, snow peas, scallion and cucumber in large serving bowl; set aside.
In another bowl, whisk together vinegar, soy sauce, ginger, sugar and pepper flakes until sugar is dissolved. Add ⅓ cup oil in a slow stream, whisking constantly, until thickened and emulsified: set aside.
For the chicken: Whisk together egg and hoisin sauce in a shallow bowl; add chicken and turn until coated on all sides. Combine sesame seeds, cornstarch and salt in a shallow bowl. Thread chicken onto skewers and roll in sesame mixture, coating well on all sides.
Heat remaining 2 tbsp oil in a large nonstick skillet over moderate heat. Add skewers and cook, turning occasionally, until browned on all sides and chicken is cooked through, 10 to 12 minutes.
Pour dressing over ginger slaw and toss until coated well; serve with warm chicken skewers.
You can grill the skewers on an outdoor grill. Use a grill pan on top of the grates so the sesame coating doesn't come off as it cooks.