Prepare the poaching liquid. Combine 1 cup white wine, 3 cups water, 1 halved, peeled shallot, and 1 tsp peppercorns in a medium saucepan. Zest the lemon, then reserve and set aside. Slice the lemon in half, squeeze the juice directly into the pan, then place lemons halve inside. Bring to a boil over high heat.
Poach the salmon. When boiling, add skinless salmon fillet to the poaching liquid. Cook for 10 minutes, or until fully cooked through. Gently remove the cooked salmon to a plate and discard the poaching liquid. Allow to cool slightly, then flake the salmon into small pieces.
Sauté the shallot. While the salmon is cooking, heat 1 Tbsp butter in a skillet over medium heat, no higher. Mince the remaining shallot, then add to the warm pan. Cook until softened and translucent, about 5 minutes, stirring often. Set aside.
Mix remaining ingredients. In a large mixing bowl, combine remaining 3 Tbsp butter, 2 Tbsp sour cream, chopped smoked salmon, 2 Tbsp chives, 2 Tbsp chopped dill, 1 Tbsp capers, 1 Tbsp olive oil, ¼ tsp sweet paprika, reserved lemon zest, and the cooked shallots. Use a spatula to gently combine.
Add cooled salmon. Add the poached salmon to the bowl, then stir to gently combine.
Chill the rillettes. Transfer the salmon rillettes to one or two glass containers, then seal with a tight fitting lid or wrap well with plastic wrap. Refrigerate for at least 2 hours to firm up.
To serve: Take out the fridge about 15-20 minutes before serving (easier to spread at room temperature), then serve on crackers, sliced baguette, or endive leaves.