Scrub mussels well and remove beards. Squeeze enough juice from limes to measure 1/3 cup. In an 8-quart kettle boil lime juice, coconut milk, wine, curry paste, garlic, fish sauce, and sugar over high heat, stirring, 2 minutes. Add mussels, tossing to combine. Cook mussels, covered, stirring occasionally, until opened, about 5 to 8 minutes. (Discard any unopened mussels.) Chop cilantro and toss with mussels.
Serve mussels with lime wedges.