In a mixing bowl, whisk together the lime juice, soy sauce, lime zest, minced ginger, rice vinegar, and honey; set the sauce aside.
Heat the large skillet or wok over medium heat and add the vegetable oil and 1/2 tablespoon sesame oil.
Add the diced chicken and sauté, turning occasionally, until browned and no longer pink, about 4 minutes total.
Stir the reserved lime sauce into the coconut milk and red curry paste until combined, then pour into the skillet with the chicken and cook for 3 minutes.
Fold in the sliced shiitake mushrooms, snow peas, and diced mango; reduce heat to low and simmer about 10 minutes, until the sauce thickens and vegetables are tender-crisp.
Add the remaining 1 tablespoon sesame oil, stir to combine, and remove from heat.
Serve garnished with cashews, cilantro, and optional coconut flakes.