Preheat the oven to 375 degrees.
Line a sheet pan with parchment paper.
Squeeze the sauerkraut to get rid of as much of the liquid as possible, then blot dry with a paper towel.
Lightly dust a work surface with flour and unfold the puff pastry.
Roll the pastry dough into an 8-by-12-inch rectangle, and cut in half lengthwise, so you end up with 2 4-by-12-inch rectangles.
Cut each of the smaller rectangles into thirds so you end up with 6 squares, each measuring 4-by-4 inches.
Cut each square into 1-inch strips. (You should have 24 strips of dough.)
Spread a small dollop of the onion relish onto one end of each strip of dough. (Save any leftover relish to serve alongside the pigs.)
Place a small pinch of sauerkraut on the relish, and nestle a hot dog piece on top.
Starting with the end where the filling is, roll up the pigs, and place them seam side down on the prepared sheet pan.
In a small bowl, beat an egg with 2 teaspoons of water.
Brush the pastry with egg wash, and let the pigs chill in the refrigerator for 15 to 20 minutes.
Bake until the pastry is golden brown and puffy, 20 to 25 minutes.
Let cool slightly, and serve with the mustard, and any leftover onion relish, for dipping.