Grease grill grates with oil then preheat grill to medium heat. Brush salmon all over with oil then season with salt and pepper. Arrange salmon on grill, skin-side up, and cook, gently flipping once, until golden brown and just cooked through, 8 to 10 minutes total. Set aside to let cool then remove and discard skin.
Put cottage cheese, lemon juice and horseradish (if using) into a food processor and purée until smooth; transfer mixture to a large bowl. Flake salmon into small pieces and add to cottage cheese mixture along with 2 tablespoons of the chives and fennel bulb and fronds. Fold gently to combine then garnish with remaining 1 tablespoon chives and serve.
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