Pat shrimp dry and chop into small pieces.
Warm olive oil in a skillet over medium heat. Sauté shrimp until opaque, about 2–3 minutes. Let cool completely.
Beat softened butter in a bowl until creamy and light.
Stir in garlic, lemon zest, smoked paprika, cayenne, Worcestershire, and hot sauce until evenly blended.
Fold in cooled shrimp, parsley, chives, and lemon juice. Season with salt and black pepper to taste.
Scoop butter onto plastic wrap, form a log, and chill until firm, about 30 minutes. Alternatively, pack into a ramekin.
Serve spread on warm toast, melted over grilled steak or fish, or tossed with hot pasta.