Stir together gingersnaps and milk in a medium bowl. Let stand until cookies are softened (about 10 minutes).
Cut squash in half lengthwise; remove seeds. Line a baking sheet with aluminum foil. Coat foil with cooking spray. Place squash, cut side down, on foil. Bake, uncovered, at 400° for 30 to 40 minutes or until tender. Scoop out pulp; mash. Discard shell. Measure 1 3/4 cups pulp; reserve any remaining pulp for another use.
Stir 1 3/4 cups squash pulp, 1/2 cup cheese, butter, and salt into softened gingersnaps. Working with 6 won ton wrappers at a time (keeping remaining wrappers covered), spoon about 1 tablespoon squash filling into center of each wrapper. Moisten edges of each wrapper with water; bring 2 opposite corners together. Press edges together with a fork to seal, forming a triangle. Cover ravioli with a damp towel to keep them from drying.
Bring 2 quarts water to a boil in a large saucepan. Cook ravioli, 6 at a time, uncovered, 1 to 2 minutes. Quickly remove from water with a slotted spoon. Keep warm. Place 6 ravioli in each serving bowl. Top each with 1 tablespoon Sage Butter Sauce. Sprinkle evenly with remaining 1/2 cup cheese and pepper.