Bake the potato puffs as the label directs. Sprinkle with 1/2 teaspoon celery salt.
Meanwhile, whisk the vinegar and mustard in a large bowl. Whisk in 3 tablespoons vegetable oil until smooth. Add the lettuce, cucumber, tomatoes and sliced pepperoncini; season with celery salt to taste. Toss to combine.
Slice the hot dogs lengthwise about three-quarters of the way through; open like a book. Heat the remaining 1 tablespoon vegetable oil in a large skillet over medium-high heat. Add the hot dogs cut-side down. Cook until browned and crisp, 2 to 3 minutes. Flip and cook until browned on the other side, about 2 minutes.
Divide the salad among plates; top each with a hot dog. Drizzle some mustard on the hot dogs, then top with the onion and relish. Add the potato puffs and whole pepperoncini.