Make the Russian dressing: In a bowl, whisk together the mayonnaise, ketchup, prepared horseradish, Worcestershire sauce, lemon juice, paprika, hot sauce, finely grated onion, kosher salt, and black pepper until smooth.
Prep the sauerkraut: Place the drained, squeezed-dry sauerkraut in a dry skillet over medium heat and cook, stirring, until steaming and excess moisture has evaporated, 3–5 minutes; transfer to a bowl.
Warm the corned beef: Add the thinly sliced corned beef to the same skillet over medium-low heat, cover, and warm until hot and pliable, 2–3 minutes; remove from the heat.
Lay out the rye bread and spread Russian dressing on one side of each slice.
Build the sandwiches: Place 2 slices of Swiss cheese on each of 4 dressed bread slices, then evenly pile on the warm corned beef and top with the warmed sauerkraut. Close with the remaining bread, dressing side down.
Butter the outsides of each sandwich with the softened butter.
Griddle the sandwiches in a large skillet or on a griddle over medium heat until the bread is deep golden and crisp and the cheese is melted, 3–4 minutes per side. Reduce heat if browning too quickly and press gently with a spatula for even contact.
Rest 1 minute, slice each sandwich in half, and serve hot with dill pickle spears.