In a large bowl, whisk together the plain yogurt, lemon zest, fresh lemon juice, cumin, salt, black pepper, minced garlic, and dried oregano.

Mix until smooth, ensuring all ingredients are well incorporated.

Add the boneless chicken pieces to the marinade, tossing them to ensure they are completely coated.

Cover the bowl with plastic wrap and refrigerate for at least 1 hour, up to 24 hours.

Grate the cucumber, squeeze out excess water, and combine with yogurt, minced garlic, dried oregano, fresh dill, lemon juice, salt, and black pepper.

Mix well, refrigerate until serving.

Soak wooden skewers in water for about 5 minutes before cooking.

Thread 4-5 pieces of marinated chicken onto each skewer.

For grilling, preheat to medium-high heat and cook skewers for 5-6 minutes on each side.

For baking, preheat oven to 400°F and bake skewers for 12-15 minutes.

Serve warm alongside tzatziki sauce for dipping.