In a 12-inch skillet heat 3 tablespoons of the olive oil over medium-high heat. Cook wonton strips in hot oil until browned, stirring occasionally. Using a slotted spoon, transfer wonton crisps to paper towels to drain; set aside.
Lightly season tuna with salt and pepper. In the same hot skillet cook tuna for 3 to 4 minutes per side or until some pink remains in center. Transfer tuna to a cutting board; slice tuna for salads.
For dressing, whisk together remaining olive oil, vinegar, sugar, and lime peel. Divide cabbage, sliced tuna, and cucumber among shallow bowls. Top salads with dressing and wonton crisps.