Heat the sesame oil and olive oil in a large skillet over medium-high heat.
Add the diced chicken to the hot skillet and cook, turning occasionally, until cooked through, about 5 minutes.
Stir in the minced garlic and ground ginger and cook for about 1 minute, until fragrant.
Add the coleslaw mix to the skillet, pour in the soy sauce (use 2/3 cup for a saucier dish), add the hoisin sauce and black pepper, and stir to combine.
Cook the cabbage mixture, stirring occasionally, until the cabbage is wilted and tender, about 5 minutes; during the last 2 minutes, add the sugar snap peas and cook until crisp-tender.
Remove the skillet from the heat, fold in the drained mandarin oranges, and taste; stir in honey if desired.
Garnish evenly with sliced green onions and serve immediately.