Wash the cucumber and cut it into thin strips. Pluck the mint leaves and roughly chop them. Halve the lime, squeeze out the juice and mix it in a small bowl with the fish sauce to make a liquid dressing.
Bring a pot of water to a boil and cook the rice noodles until tender. Drain the noodles, rinse them immediately with cold water so they cool and don't stick together, and let them drain well. Meanwhile, heat a skillet and cook the shrimp for a few minutes until they turn pink all over and are completely cooked through.
Put the cooled rice noodles in a large bowl. Add the cucumber strips, freshly chopped mint and cooked shrimp. Pour the fish sauce and lime dressing over everything and toss all the ingredients together thoroughly so the flavors blend well.
Divide the salad into equal portions onto the plates. Serve the dish immediately so the contrast between the warm shrimp and the fresh noodle salad is at its best.