Rinse the limes in hot water and grate them dry. Cut 4 small spirals out of the lime peel with the chiseler and place them in cold water. Halve the limes and squeeze the juice. For the coconut edge, pour the juice of 1 lime and grated coconut separately onto 2 small plates.
Dip the edge of the glass first in lime juice, then in the grated coconut. Leave to dry.
Pour coconut water, coconut milk, remaining lime juice and agave syrup into a shaker, fill up with tequila and lime juice, add crushed ice and shake well. Divide coconut margarita into glasses, decorate with lime spiral and serve.