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.