Add mayonnaise, cream cheese, mustard, and chiles to a small bowl and mix until smooth.
Heat tortillas according to package directions. On each warm tortilla evenly spread 1 1/2 teaspoons of the mayonnaise mixture and top with salami. Spread another 1 1/2 teaspoons of mayonnaise mixture over the salami and top with a lettuce leaf keeping layers as even as possible.
Gently roll up each tortilla tightly and trim ends. Wrap each roll in plastic wrap and refrigerate at least 30 minutes before serving. When ready to serve cut each roll into eight pieces and secure each piece with a cocktail toothpick.