In large pot bring white wine to simmer. Add mussels and cover. Cook until mussels open ~ 5 min. Drain and let cool. Discard any unopened mussels.
Break off and discard empty halves of mussel shells and loosen mussels from other halves. In separate container toss cucumber, red peppers, oils, red onion, parsley, lemon juice, capers and season with salt and pepper. Spoon over mussels and serve.