Magento 2 Order ID – Correct Way to Change Default Order ID

As stated in the comments the script you have should work nicely for magento version 1.4+.
In the 1.4 version the sales entities were mapped to flat tables that have constraints so everything should cascade nicely.

For versions prior to 1.4 all the entities related to sales (orders, invoices, shipments and creditmemos) were EAV and kept in the same tables. So nothing cascade.
For version prior to 1.4 you can try this script.
This should work for later versions also but I don't think it's needed.

$orders = Mage::getModel('sales/order')->getCollection()
    ->addFieldToFilter('entity_id', (array) $orderIds);
foreach ($orders as $o) {
    //load order object - I know it's not ok to use load in a loop but it should be ok since it's a one time script
    $order = Mage::getModel('sales/order')->load($o->getId());

    $invoices = $order->getInvoiceCollection();
    foreach ($invoices as $invoice){
        //delete all invoice items
        $items = $invoice->getAllItems(); 
        foreach ($items as $item) {
            $item->delete();
        }
        //delete invoice
        $invoice->delete();
    }
    $creditnotes = $order->getCreditmemosCollection();
    foreach ($creditnotes as $creditnote){
        //delete all creditnote items
        $items = $creditnote->getAllItems(); 
        foreach ($items as $item) {
            $item->delete();
        }
        //delete credit note
        $creditnote->delete();
    }
    $shipments = $order->getShipmentsCollection();
    foreach ($shipments as $shipment){
        //delete all shipment items
        $items = $shipment->getAllItems(); 
        foreach ($items as $item) {
            $item->delete();
        }
        //delete shipment
        $shipment->delete();
    }
    //delete all order items
    $items = $order->getAllItems(); 
    foreach ($items as $item) {
        $item->delete();
    }
    //delete payment - not sure about this one
    $order->getPayment()->delete();
    //delete quote - this can be skipped
    if ($order->getQuote()) {
        foreach ($order->getQuote()->getAllItems() as $item) {
            $item->delete();
        }
        $order->getQuote()->delete();
    }
    //delete order
    $order->delete();
}

Use \Magento\Sales\Api\OrderRepositoryInterface::get and \Magento\Sales\Api\OrderRepositoryInterface::save. This is public API of sales module and after future Magento releases will not change, so your custom module will not be broken.

Magento 1 style (manipulations with models an resource models directly from third party modules) should not be used in case when suitable public API is available (such classes/methods are marked with @api tag). Such approach will lead to custom module being broken after the next Magento 2 releases.