Heat the cooking oil in a frying pan or wok. Add the carrot and chayote. Saute for about a minute. Pour in the wine. Boil uncovered until the wine is reduced to almost nothing and the vegetables are cooked through but not mushy. Depending on the age of the vegetables (younger ones are more tender and cook faster), this stage takes anywhere from five to 10 minutes.
If the wine dries up before the vegetables are done, add half a cup of water and continue boiling until quite dry. Don’t worry about the “dry” state — the shrimps will render their natural juices so you still get a nice amount of sauce.
When the vegetables are done, add the shrimps, the garlic, ginger and chilis. Stir fry over very high heat just until the shrimps change color. Turn off the heat. Season with salt. Transfer the cooked dish to a serving plate. Garnish with fine slivers of green onion. Serve at once.