Make the sauce. In a small bowl, whisk together mayonnaise, no-sugar-added ketchup, relish, vinegar, paprika, and a pinch of salt and pepper. Adjust to taste. Cover and chill while you prepare the bites.
Prep the sauerkraut. Place sauerkraut in a clean kitchen towel and squeeze out as much moisture as possible.
This step prevents sogginess and keeps the bites crisp.
Sauté the filling. Heat butter or oil in a skillet over medium. Add corned beef, drained sauerkraut, caraway seeds (if using), and black pepper. Cook for 3–5 minutes, stirring, until warm and lightly browned.
Remove from heat and fold in 1 cup of the shredded Swiss to help bind the mixture.
Make cheese cups or crisps (option A). Preheat oven to 375°F (190°C). Line two baking sheets with parchment. Place 12–16 mounds (1–2 tablespoons each) of shredded Swiss with a pinch of mozzarella for structure, spaced well apart.
Bake 6–8 minutes, until bubbly and golden at edges. While hot, drape each round over the underside of a mini muffin tin or gently press into silicone mini molds to form cups. Let cool to set.
Use low-carb mini wraps (option B). If using mini tortillas/wraps, preheat oven to 375°F (190°C).
Lightly grease a mini muffin pan. Press wraps into wells to form cups and bake 6–8 minutes until crisp and lightly golden. Cool slightly.
Assemble the bites. Spoon the warm corned beef mixture into the cheese cups or baked wraps.
Top with a pinch of the remaining Swiss. Return to the oven for 2–3 minutes, just until the cheese melts.
Finish with sauce. Drizzle or dollop a little Keto Thousand Island over each bite. Add chopped chives or parsley for a fresh pop of color.
Serve. Enjoy warm.
Offer extra sauce on the side for dipping.