Preheat oven to 400. Line baking sheets with parchment paper. In a small bowl, whisk together egg and water.
Unfold 1 pastry sheet on a lightly floured surface. Roll pastry sheet into a 12"-inch square. Cut into 16 (3-inch) squares. Spoon about 1 teaspoon relish in center of each square. Place 1 cocktail wiener diagonally on top of relish. Brush edges of squares with egg mixture. Fold 2 opposite corners to the center over wiener, and pinch firmly to seal. Repeat procedure with remaining puff pastry sheet, relish, and cocktail wieners. Place filled pastries on baking sheets.
Bake for 15 minutes, or until pastries are golden brown.