Meanwhile, stir together vinegar, mirin, and sugar in a small microwave-safe bowl. Microwave on HIGH in 30 second intervals, stirring between each, until sugar is dissolved.
Add vinegar mixture to rice and stir gently until absorbed. Divide rice among 6 bowls.
Steam snow peas according to package directions; cool slightly.
Top rice mixture with shrimp, cucumber, avocado, snow peas, and ginger.
