I love chayote. I think a lot of people simply don't understand what it is. It is a tropical, vegetable-like fruit that kind of tastes like a jícama or a pear or a cucumber. Since it is almost like a combo of a squash and a pear, it makes a great slaw. With the sherry vinegar added, there's a nice balance of sweet and tart that is great with grilled shrimp.
Place 12 wooden skewers in a shallow dish, cover with hot water, and set aside to soak. Preheat a gas or charcoal grill to medium heat or heat a grill pan over medium heat.
Bring a small saucepan of salted water to a boil. Cut the chayotes in half and carefully remove the pits with a paring knife.
Drop the chayotes into the water, bring back to a boil, and reduce the heat to medium. Cook the chayotes, until a skewer goes through but the chayotes still hold their shape, about 3 minutes.
Drain and let cool.
Coat the blanched chayote halves with a little bit of olive oil. Add the chayote halves to the grill or grill pan, cut side down, and grill until grill marks appear, 2 to 3 minutes. Turn the pieces over and grill until nice grill marks appear, another 2 to 3 minutes. (You can skip the grilling of the chayotes, but it adds nice flavor and color.) Cut into small dice.
To thread the shrimp onto the skewers: Drain the skewers. Nestle together 3 shrimp, then put a skewer through the thick parts, skewering each shrimp. Then put another skewer straight through the thinner parts.This not only stabilizes the shrimp, but gives you a nice handle for grilling.
Using a basting brush, coat the shrimp on both sides with about 2 tablespoons olive oil. Season with salt and freshly ground pepper. Grill until cooked through, for 2 to 3 minutes on each side. Remove the shrimp from the skewers and set aside to cool, then refrigerate.
In a large bowl, combine the diced chayote, onion, tomato, red pepper, and cilantro. Add about 3/4 cup olive oil and the vinegar and season with about 1 tablespoon salt and 1 teaspoon pepper. Toss and check for seasoning. Cover and marinate in the refrigerator for at least 2 hours before serving.
Divide the salad among 6 plates, topping each serving with 3 shrimp. Garnish with cilantro sprigs and serve.