Tear bread into chunks, and place in a food processor. Pulse to make fresh bread crumbs. Transfer crumbs to bowl; set aside. Place tuna in processor, and pulse 5 seconds. Return crumbs to processor; add green onions, cream of coconut, ginger, garlic, salt, sesame oil, and lime juice; pulse to blend. Shape mixture into 4 patties. Heat grill.
In small jar with tight-fitting lid, combine oil, vinegar, sugar, salt, and sesame oil; shake well. In large bowl, toss together cabbage, radishes, carrots, and green onions.
Spray patties with vegetable cooking spray, and grill over medium-high heat for 3 minutes per side. Toss salad with dressing. Serve tuna burgers with salad.