Combine first 6 ingredients in a large zip-top plastic bag; seal. Marinate in refrigerator 24 hours, turning occasionally.
Remove steak from bag, and discard marinade. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Add steak to pan; grill 6 minutes on each side or until desired degree of doneness. Remove steak from pan; let stand 10 minutes. Cut steak diagonally across grain into thin slices; cut slices into 2-inch pieces.
Combine mayonnaise, wasabi paste, and vinegar, stirring well. Spoon 3/4 teaspoon mayonnaise mixture onto each cracker. Divide steak evenly among crackers; top each with 1/4 teaspoon mayonnaise mixture. Garnish with chives, if desired.
Mirin is a kind of Japanese rice wine similar to sake but with a lower alcohol content. It's a clear, gold liquid that adds a mild sweetness to dishes and a slight sheen to meats, fish, and shellfish.