In a pitcher, muddle the sugar cubes, cucumber wheels, kaffir lime leaves, and salt with the club soda until the sugar is fully broken up.
Add the remaining ingredients and fill the pitcher three-quarters full with ice cubes.
Stir until cold, then strain into a punch bowl over 1 large block of ice.
Garnish with the cucumber wheels and kaffir lime leaves and serve with a ladle and punch glasses.