Bring a large pot of water to a boil. Carefully add the potatoes and corn rounds to the boiling water to prevent splashing. Boil for 6-7 minutes, or until the potatoes are fork-tender, then drain.
Immediately transfer the potatoes and corn to a large bowl of ice water to stop the cooking. Let them cool completely, then drain again and pat dry with a clean kitchen towel or paper towels.
To a large mixing bowl, add the potatoes, corn, kielbasa, and zucchini. Drizzle with olive oil. Sprinkle with kosher salt, black pepper, garlic powder, and cayenne pepper. Toss gently until all ingredients are evenly coated with oil and seasonings.
Thread the potatoes, corn, kielbasa, and zucchini onto the skewers, alternating as desired. Repeat the pattern 2 or 3 times per skewer, depending on skewer size. Leave a little space at each end of the skewer for easy handling. Set the assembled skewers aside.
Preheat grill to medium-high heat (about 400°F).
Clean and lightly oil the grill grates. Place the skewers directly over the heat.
Grill the skewers for 10 to 12 minutes total, turning every 3 to 4 minutes, until the kielbasa has good grill marks and the vegetables are tender and slightly charred. (Move the skewers to indirect heat if any pieces begin to char too quickly.)
While the skewers are cooking, heat the cowboy butter in the microwave in 30-second increments, stirring in between, until melted and warmed through. Stir well to combine.
As soon as the skewers come off of the grill, brush the warm cowboy butter generously over them.
Serve immediately with extra cowboy butter on the side for dipping.