Scrub clams and mussels; pull beards off mussels if still attached. Discard any clams and mussels that don't close when you tap their shells.
Pour olive oil into a 10- to 12-inch frying pan over medium-high heat; when hot, add shallots, ginger, and garlic and stir often until shallots are limp, 2 to 3 minutes. Stir in coconut milk, wine, and chili sauce and bring to a boil.
Add clams, cover, and cook for 5 minutes. Add mussels, cover, and simmer, reducing heat if necessary, until all the shells have opened, 2 to 3 minutes longer. Gently stir in lime juice and basil; add salt to taste.
Pour into a large bowl for sharing, or ladle into individual bowls. Sprinkle green onions on top and garnish with lime wedges.