Peel and coarsely grate the potatoes. Working in batches, heat 2 teaspoons of the butter with 2 teaspoons of the vegetable oil in a large nonstick skillet over medium-high heat until very hot. Sprinkle 2 tablespoons of the potatoes into the pan, pressing into a 3-inch diameter with a spatula to create lacy, flat rounds of potato. Don't be concerned if you can see the bottom of the pan through gaps in the potatoes. Cook until well browned on each side, pressing down firmly. Season with salt while hot. (The cakes can be made several hours in advance and crisped in a hot oven before serving.)
Combine the creme fraiche, lemon juice, and horseradish in a small bowl and season with salt and pepper, to taste. Arrange 3 pancakes per serving on small plates. Top the pancakes with equal amounts of smoked salmon, a spoonful of horseradish cream, and a spoonful of caviar. Top with a few pickled onions and serve.
To make the Pickled red onions: Combine the onions, vinegar, garlic, sugar, pickling spice, and salt in a small saucepan. Bring to a boil over high heat. Reduce the heat to medium and simmer for 2 minutes. Remove from heat and cool to room temperature before serving. Chop fine.