Stir together the lemon juice, rice vinegar, soy sauce, sugar, chile, garlic and 1 tablespoon water in a small bowl. Set aside.
Slice one cocktail frank almost all the way in half lengthwise, leaving the top quarter of the frank intact. Rotate 90 degrees and slice again so you have 4 strips attached to the unsliced top of the frank. Using a sharp paring knife, cut each of the 4 strips in half so you have 8 "tentacles." Spread the tentacles and place upright on a microwave-safe plate. Repeat with the remaining cocktail franks, using 2 plates to lay out all the octopi. Microwave one plate at a time for about 30 seconds, or until the cocktail franks sizzle and the tentacles curl slightly. Let cool. The franks will keep the shape that they were microwaved in.
Heat 1 1/2 inches of oil to 360 degrees F in a heavy-bottom pot or Dutch oven. Place the cornstarch in a shallow bowl. In a second bowl, whisk together the flour, seltzer, egg and 1/4 teaspoon salt until smooth. Add the ice cubes to keep the batter cold.
Working in batches, dredge the octopi in the cornstarch, tapping off the excess, and then drag through the batter. Let the excess batter drip off so the tentacles stay defined. Carefully add to the hot oil, holding each octopus by one of the tentacles for the easiest dipping. Fry, turning, until golden brown, 3 to 4 minutes. Transfer to a paper-towel-lined plate to drain.
Serve with the dipping sauce and sliced cucumbers.