Combine almonds and sugar in a food processor and pulse until coarsely ground. Using your hands, crumble wafer cookies into almond mixture. Add cocoa powder, and pulse to grind into crumbs. Transfer to a large bowl.
Stir in corn syrup and chocolate milk. Let dough rest for 30 minutes. Make 24 balls, about 1-1/4 inch in diameter, for spider bodies, rolling in crystal sugar as you go. Make 24 balls, about 1 inch in diameter, for spider heads, also rolling in sugar. For each spider, cut eight 3-inch pieces of licorice lace for legs and a 1-inch piece to attach head to body.
Stick legs into bodies, and attach heads with licorice pieces. Pipe eyes and mouths using tubed icing.