Virtually seedless English cucumbers are available in supermarkets, shrink-wrapped for freshness. Choose firm cucumbers with brightly colored skin, free of soft spots or shriveling. Look for unblemished avocadoes that are heavy for their size and that yield to gentle palm pressure. To speed ripening, place avocadoes in a paper bag at room temperature for several days.
Combine cucumber and scallion together in a medium bowl. Whisk together vinegar and next 5 ingredients in a small bowl. Pour vinaigrette over cucumber mixture, and season with salt and pepper. Add avocado just before serving, and toss gently to mix. (You can make this salsa ahead of time and refrigerate until ready to serve, but add the avocado just before serving.)