To retrieve a list of product SKUs in random order using Magento 2's ProductRepository and SearchCriteriaBuilder, you can modify your code to include a random sort order. Here's how you can achieve this:

```php
use Magento\Framework\Api\SearchCriteriaBuilder;
use Magento\Catalog\Api\ProductRepositoryInterface;
use Magento\Framework\Api\SortOrder;
use Magento\Framework\ObjectManager\ConfigLoaderInterface;

class YourClass
{
    /**
     * @var ProductRepositoryInterface
     */
    protected $productRepository;

    /**
     * @var SearchCriteriaBuilder
     */
    protected $searchCriteriaBuilder;

    /**
     * @var ConfigLoaderInterface
     */
    protected $configLoader;

    public function __construct(
        ProductRepositoryInterface $productRepository,
        SearchCriteriaBuilder $searchCriteriaBuilder,
        ConfigLoaderInterface $configLoader
    ) {
        $this->productRepository = $productRepository;
        $this->searchCriteriaBuilder = $searchCriteriaBuilder;
        $this->configLoader = $configLoader;
    }

    public function getRandomProductSkus()
    {
        // Create a random sort order
        $sortOrder = new SortOrder();
        $sortOrder->setField('rand'); // 'rand' is not a native Magento field; you'll need to create a custom attribute for random sorting.

        // Set the random sort order in the search criteria
        $this->searchCriteriaBuilder->addSortOrder($sortOrder);

        // Build the search criteria
        $searchCriteria = $this->searchCriteriaBuilder->create();

        // Get the list of products
        $productList = $this->productRepository->getList($searchCriteria);

        // Extract SKUs from the products
        $skus = [];
        foreach ($productList->getItems() as $product) {
            $skus[] = $product->getSku();
        }

        return $skus;
    }
}
```