Place grated ginger in a square of moistened cheesecloth folded double; squeeze the juice into a small bowl and discard the pulp; set aside until needed. Weave a strip of orange peel and a fresh cranberry onto each cocktail pick. Moisten the rim of each chilled glass with a wedge of lime, then gently press into the sanding sugar.
Fill a metal cocktail shaker with cracked ice; place the top on the shaker and shake for about 10 to 15 seconds. Add vodka, orange-flavored liqueur, cranberry juice, ginger juice, and lime juice and shake for another 15 seconds. Strain the liquid into the prepared glasses and serve immediately.
Makes 4 cocktails.