Place the first eight ingredients in a large bowl; toss to combine. In a small bowl, gently toss avocados with lime juice; add to cabbage mixture. Refrigerate until serving. In a small bowl, mix honey mustard ingredients.
For burgers, place a fourth of the salmon in a food processor. Add lime peel and mustard; process until smooth. Transfer to a large bowl.
Place remaining salmon in food processor; pulse until coarsely chopped and add to puree. Fold in shallot, cilantro, soy sauce, honey, garlic, salt and pepper. Shape into four 1/2-in.-thick patties.
Moisten a paper towel with cooking oil; using long-handled tongs, rub on grill rack to coat lightly. Grill burgers, covered, over medium heat or broil 4 in. from heat 4-5 minutes on each side or until a thermometer reads 145°.
Serve on buns with honey mustard; top each with 1/2 cup slaw. Serve remaining slaw on the side. Yield: 4 servings.