Preheat a grill or grill pan to medium-high. In a shallow dish, mix 2 tablespoons vegetable oil and the tamari, lime peel, lime juice, hot pepper sauce and ginger. Add the salmon and marinate, turning occasionally, for 15 to 20 minutes.
In a bowl, whisk the vinegar, honey, sesame oil and remaining 2 tablespoons vegetable oil. Add the cabbage and toss to coat evenly. Add the chives and sesame seeds; season to taste with salt and pepper.
Grill the salmon for 3 minutes on each side for medium-rare, 4 minutes on each side for fully cooked. Serve on top of the slaw.