Blanch peas in 2 batches in a large saucepan of boiling salted water 1 minute. Transfer to a colander and rinse under cold running water to stop cooking. Drain peas well and pat dry.
Whisk together mayonnaise, soy sauce, sugar, lemon juice, and wasabi paste until sugar is dissolved. Serve sugar snap peas with dip.
Cooks' note: Peas and dip may be prepared 1 day ahead and chilled, covered.