Make the lemon-chive cream cheese by mixing the cream cheese with lemon juice, finely chopped chives, and a pinch of salt and pepper in a small bowl. Taste it and adjust the salt and pepper to your preference. Overseason this slightly so that it accounts for the lack of seasoning on the cucumber and avocado.
To each tortilla, add the ingredients in the following order: lemon and chive cream cheese, smoked salmon, sliced avocado, and cucumber.
Wrap the tortillas tightly around the filling.
Cut them in half and either serve now or refrigerate the wraps for later.