Preheat oven to 250°. Fill a deep pot with 2 in. oil, insert a deep-fry thermometer, and heat to 375° over medium-high heat.
Mix together flours, cornmeal, baking soda, and 1 tsp. salt in a medium bowl. Slowly whisk in club soda until blended.
Dip a large handful of green beans into batter. Using tongs, lift beans from batter, letting a little of excess drain, and lower a portion at a time into oil. Fry until golden brown, about 1 minute. Transfer to a large baking sheet lined with paper towels, salt to taste, and put in oven to keep warm. Repeat with remaining beans and the shallots; keep oil between 375° and 385°.
Stir together mayonnaise with chili powder in a small bowl for dipping.
Note: Nutritional analysis is per serving.