Place chicken breasts on cutting board. Trim chicken as needed, then cut chicken into 1-inch cubes. Once all chicken has been cut, season pieces on all sides with salt and pepper to taste. Set chicken aside.
Add olive oil, white wine, and lemon juice to mixing bowl. Whisk until ingredients are well-combined, then add seasoned chicken pieces to bowl. Cover with lid or plastic wrap and place bowl in refrigerator. Marinate at least 1 hour, but no more than 12 hours.
When chicken has marinated for desired length of time, remove bowl from refrigerator and drain marinade from bowl. Set chicken aside.
Add Italian breadcrumbs and panko to large shallow bowl. Mix breadcrumbs together until well-blended, then place pieces of marinated chicken in bowl, working in batches as needed. Flip and turn chicken to fully coat all sides in breadcrumbs, lightly pressing chicken into crumb mixture to ensure crumbs stick.
Slide 4 to 5 pieces of breaded chicken onto skewer, then place skewer on plate and set aside. Repeat process with remaining chicken pieces, until all chicken has been breaded and skewered.
Heat grill pan to medium-high heat. When pan is warm, lightly grease pan with cooking oil.
Place chicken skewers on grill pan, working in batches as needed to avoid over-crowding. Cook 4 to 5 minutes, then flip skewers over and cook 4 to 5 minutes more, or until chicken is cooked through and internal temperature reads 160° Fahrenheit when checked with meat thermometer.
Once chicken is cooked through, transfer skewers to plate and set aside. Repeat with remaining skewers until all chicken is fully cooked.