Preheat a grill or grill pan to medium high. Make the dressing: Whisk the vinegar, soy sauce, honey mustard and ginger in a medium bowl, then add the vegetable and sesame oils in a slow stream, whisking until combined. Toss the chicken with 1/4 cup of the dressing in another bowl; let marinate 10 minutes at room temperature. Remove the chicken from the marinade (discard the marinade) and grill until cooked through, 4 to 5 minutes per side. Transfer to a cutting board; let rest 5 minutes. Meanwhile, toss the cabbage, carrot, scallions and snow peas with the remaining dressing in a large bowl. Cut the chicken into 1/2-inch pieces and toss with the salad. Season with salt. Top with the chow mein noodles.