In a small bowl, combine broth, soy sauce, hoisin sauce, lime juice, ginger, rice vinegar, and chili paste. Reserve 3 tbs of the sauce for noodles.
Heat grill to medium-high heat. Lightly oil grill grates. Drizzle sauce on both sides of fish and brush to coat. Grill for 4 minutes on flesh side. Turn and drizzle and brush generously again with sauce; grill for an additional 4 minutes on skin side or until fish flakes easily. Drizzle any remaining sauce over top. Gently remove from grill with a large spatula.
While fish is grilling, lightly spritz bok choy with nonstick cooking spray and season with salt. Grill for 3 minutes per sie or until lightly charred and tender.
Meanwhile, cook pasta following package directions, about 7 minutes. Drain; stir in red pepper, half the scallions and the reserved 3 tbs sauce.
Serve fish immediately with noodles and bok choy. Squeeze lime wedges over each portion and sprinkle remaining scallions on top.