Mist 24 mini-muffin cups with cooking spray. Place 1 sheet of phyllo on work surface; mist sheet all over with cooking spray. Top with second sheet; mist with cooking spray. Top with third sheet; mist with cooking spray. Cut lengthwise into 4 strips and crosswise into 6 strips (for a total of 24 pieces). Press each piece into prepared mini-muffin cup. (If preparing in batches, keep remaining squares covered with a lightly damp cloth to keep from drying out.)
Bake in a preheated 400°F (200°C) oven until crisp and golden, 4 or 5 minutes. Remove cups from pan and let cool on rack.
Place crabmeat in a strainer, pressing to remove excess liquid. In a large bowl, whisk mayonnaise, garlic, tomato paste, mustard, vinegar, paprika, hot sauce, salt and pepper. Add drained crabmeat, green onion, sweet pepper, parsley and capers; stir gently to combine. Spoon into baked phyllo cups.
Per cup: 42 calories, 2 g protein, 3 g fat (0 g saturated fat), 2 g carbohydrates, 0 g fibre, 10 mg cholesterol, 89 mg sodium