Wash the cucumbers, trim the ends, and peel alternating strips of skin. Cut into pieces that fit your blender. Juice the limes and discard the seeds.
Blend the cucumber pieces with some of the 4 cups cold water until smooth. Work in batches if needed, then pour everything into a large pitcher. For a smoother drink, pass the mixture through a fine-mesh strainer; leave it unstrained if you enjoy the pulp.
Stir in the lime juice, sugar, and the remaining measured water until the sugar dissolves. Taste and adjust the sweetness or dilution to your preference. Keep chilled until serving.
If desired, lightly coat the rims of the glasses with honey, then dip them in Tajín. Fill the glasses with ice, stir the pitcher, and pour in the agua fresca. Garnish with cucumber chunks.