Preheat oven to 325 degrees F (165 degrees C). Grease pint jars with 1 tablespoon shortening.
Soak raisins in hot water until plump, about 10 minutes. Drain.
Combine sugar, 1 cup shortening, and eggs in a large bowl; beat with an electric mixer until creamy. Beat in raisins. Add flour, cinnamon, baking soda, salt, and baking powder; beat until blended. Fold zucchini, walnuts, and vanilla extract into the batter.
Divide batter among greased jars, filling each one 2/3 full. Arrange jars on a rimmed baking sheet.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Turn off oven, keeping jars inside. Remove jars one at a time from the oven using oven mitts; trim off excess cake, wipe rims, and screw on lids.
Place jars several inches apart on a cloth-covered or wood surface and let cool completely, about 2 hours. Store jars in the refrigerator.