Combine cabbage and next 4 ingredients in a large bowl; set aside. Whisk together lime juice, 1/4 teaspoon salt, 1/4 teaspoon pepper, vinegar, and next 4 ingredients; set aside.
Slice squid in half lengthwise. Score squid tubes with the tip of a knife in a diamond design; pat dry. Brush tubes and tentacles with oil, and sprinkle with remaining 1 1/2 teaspoons salt and 1 1/2 teaspoons pepper.
Coat grill rack with cooking spray. Place squid on grill, scored side down. Grill squid, covered with grill lid, over medium-high heat (350° to 400°) 1 minute on each side. Remove squid from grill, and cut into 1-inch pieces. Serve warm squid over cabbage mixture, and drizzle with lime vinaigrette.
Note: You also may broil squid 1 to 2 minutes on each side or until opaque.