Peel the cucumber, cut in half lengthways, and slice crossways as thinly as possible. In a small bowl, combine the butter and orange zest and stir until creamy and blended.
Spread each slice of white bread with about 1 1/2 teaspoons of the butter mixture. Arrange several slices of cucumber on each slice and top with the whole-wheat bread. Cut each sandwich into 4 triangles.
To serve, arrange the sandwiches on a platter, alternating white and brown sides of the sandwiches and garnish with mint sprigs and orange slices.