In a mixing bowl, combine the softened cream cheese, garlic powder, onion powder, black pepper, and paprika. Mix until well blended and smooth.
Lay out a slice of salami on a clean surface. Spread a thin layer of the cream cheese mixture over the salami.
Place a few slices of green bell pepper and cucumber on one end of the salami. Sprinkle some chopped chives on top.
Starting from the end with the vegetables, carefully roll the salami tightly around the filling.
Repeat the process with the remaining salami slices and filling.
Once all roll-ups are made, slice each roll into bite-sized pieces, about 1 to 2 inches thick.
Arrange the roll-ups on a serving platter and refrigerate for at least 30 minutes before serving to allow the flavors to meld.