3 ounces freshly squeezed lime juice plus 6 lime wedges
2 cups shaved or crushed ice
Bring the sugar and coconut water to a boil in a small saucepan over medium heat. Simmer until the sugar is completely dissolved, about 2 minutes. Remove from the heat and let the coconut simple syrup cool completely. (This recipe makes approximately 3/4 cup coconut simple syrup, which can be used to sweeten other things if not used for making daiquiris.)
Add the white rum, coconut rum liqueur, lime juice, 3 to 5 ounces of the cooled coconut simple syrup (depending on desired sweetness) and the shaved ice to a large martini shaker or pitcher. Shake or stir the ingredients until thoroughly mixed. Strain into 6 chilled martini glasses and garnish the rims of the glasses with lime wedges.