Peel skin from baked and cooled potatoes and coarsely grate into a mixing bowl. Sprinkle salt, chives, garlic powder and potato starch over potatoes then toss gently to coat. Add shredded cheddar cheese then toss gently to incorporate.
Press small amount of potato mixture together in your hand (if it falls apart, add more starch in 1 tsp increments until mixture holds its form). Cut string cheese in half lengthwise, then cut into ½"– ¾" long pieces.
Place 1 heaping Tbsp of potato mixture into palm of hand and indent with thumb then place 1 piece of string cheese in center of potato mixture. Cover string cheese completely with potatoes (form a tot with the cheese in the center of the potato mixture). Continue to form tater tots, pressing firmly so they hold together. Repeat with all remaining filling and cheese.
Line baking sheet with foil or parchment paper then coat with cooking spray. Evenly space tots on baking sheet then brush with oil and bake 12−15 minutes, turning once halfway through baking.