Prep cucumber salad: Rinse the cucumber thoroughly and slice it into pieces. Add the salt to the cucumber, and stir gently to combine well. Chill in the refrigerator for 15 minutes. While chilling, prep ingredients.
Prep the garlic for the cucumber salad and all vegetables for the wrap per instruction above.
Make the cucumber salad dressing: Combine the garlic, vinegar, sugar, chili oil, and sesame oil together, and stir to mix well. Make sure that the sugar is completely dissolved. Set aside.
Make peanut sauce: Combine all the ingredients in a food processor or whisk in a bowl by hand until smooth, adding a little hot water as needed for a smooth consistency.
Make the orange ginger spritzer: mix all ingredients together.
Cook chicken: Set a grill pan or skillet over medium heat. Brush the chicken on one side with toasted sesame oil. Place the chicken seasoned side down the grill pan or skillet and brush the other side with toasted sesame oil. Cook the chicken for about 6 minutes on each side until the internal temperature reaches 160°F (74°C). Set aside to cool.
Prepare the veggies: Mix the cabbage, carrot, red bell pepper, and radishes in a large bowl. Drizzle soy sauce, olive oil, and rice vinegar over the top of the cabbage mixture and toss to fully incorporate and combine.
Make the wraps: Chop the chicken into small pieces. Spread 1-2 tablespoons peanut sauce in the center of each tortilla. Divide the cabbage mixture evenly between the wraps and top each with chicken. Fold in the edges of the tortilla then wrap and roll.
Finish the cucumber salad: Drain the salt water from the cucumber. Add the dressing to the cucumber and toss well. Top with sesame seeds and serve immediately.
Serve: Enjoy the wraps with extra peanut sauce for dipping, cucumber salad, and orange ginger spritzer (over ice if desired).