Combine the sugar, lime zest and 1/4 cup water in a small saucepan. Bring to a boil, stirring a few times until the sugar is dissolved. Chill completely before making the mojitos.
Add the mint and 1/4 cup of the chilled lime syrup to a pitcher; muddle with a wooden spoon to bruise the mint. Add the coconut water, lime juice, white rum and coconut rum and stir to combine. Refrigerate, covered, for at least 30 minutes to let the flavors meld.
Fill four glasses with ice, then fill by three-quarters with the rum mixture. Top off with lime club soda. Garnish with torn mint and serve.