Halve each egg lengthwise. Carefully remove yolks and transfer them to a fine mesh strainer set over a bowl. Transfer whites to a platter. Using a rubber spatula, press yolks through the strainer. Add mayonnaise, mustard, lemon juice, lemon zest, salt and cayenne. Whisk or stir vigorously with spatula until smooth.
Fold in flaked smoked trout, reserving a small amount for garnish. Transfer mixture to a piping bag and pipe the mixture into the well of each egg white.
Garnish with smoked paprika, chives and the remaining flaked trout.