Combine lemon juice, rice vinegar, soy sauce, sugar, chile, garlic, and 1 tablespoon of water in a small bowl to make the dipping sauce.

Set the dipping sauce aside.

Slice a cocktail frank almost in half lengthwise, leaving the top quarter intact.

Rotate the frank 90 degrees and slice again, creating 4 strips attached to the top.

Cut each of the 4 strips in half to form 8 'tentacles'.

Spread the tentacles apart and place the frank upright on a microwave-safe plate.

Repeat the process with the remaining cocktail franks.

Microwave one plate of octopi for about 30 seconds, until they sizzle and the tentacles curl slightly.

Let the microwaved octopi cool.

Heat 1 1/2 inches of vegetable oil to 360°F in a heavy-bottom pot or Dutch oven.

Place cornstarch in a shallow bowl.

In a separate bowl, whisk together flour, seltzer water, egg, and 1/4 teaspoon of salt until smooth to make the tempura batter.

Add ice cubes to the batter to keep it cold.

Working in batches, dredge each octopus in cornstarch, removing the excess.

Dip the cornstarch-coated octopus into the tempura batter, letting excess batter drip off.

Carefully add the battered octopus to the hot oil, holding it by one of the tentacles.

Fry the octopus, turning occasionally, until golden brown for 3 to 4 minutes.

Transfer the fried octopus to a paper-towel-lined plate to drain excess oil.

Serve the tempura octopus hot dog bites immediately with the prepared dipping sauce and sliced cucumbers.