In a medium bowl, combine cheese, green onion, and horseradish. Cover and chill until ready to use.
Preheat oven to 375 degree F. Unfold one of the pastry sheets on a lightly floured surface. With the tines of a fork, generously prick the pastry. Use a 2-inch triangle cutter to cut pastry into 16 triangles. Transfer triangles to an ungreased baking sheet. Lightly brush pastry with milk. If desired, sprinkle with salt. Bake for 10 to 12 minutes or until golden brown. Cool on a wire rack. Repeat with remaining pastry sheet. Do not reroll pastry scrapes.
To assemble, use a knife to split the baked pastries horizontally. Spread about 1 teaspoon of the cheese mixture onto the cut side of each bottom pastry. Top with a cucumber slice and some radish slices. Spread about 1 teaspoon of the cheese mixture onto the cut side of each top pastry. Place on top of radish slices. If desired, garnish with a small piece of thyme sprig. Makes 32 appetizers.