$OrderOBJ = wc_get_order(2343);
    $item = new WC_Order_Item_Shipping();

    $new_ship_price = 10;

    $shippingItem = $OrderOBJ->get_items('shipping');

    $item->set_method_title( "Amazon shipping rate" );
    $item->set_method_id( "amazon_flat_rate:17" );
    $item->set_total( $new_ship_price );
    $OrderOBJ->update_item( $item );

    $OrderOBJ->calculate_totals();
    $OrderOBJ->save()

$order_id = 2343;
$order    = wc_get_order($order_id);
$cost     = 10;
$items    = (array) $order->get_items('shipping');
$country  = $order->get_shipping_country();

// Set the array for tax calculations
$calculate_tax_for = array(
    'country' => $country_code,
    'state' => '', // Can be set (optional)
    'postcode' => '', // Can be set (optional)
    'city' => '', // Can be set (optional)
);

if ( sizeof( $items ) == 0 ) {
    $item  = new WC_Order_Item_Shipping();
    $items = array($item);
    $new_item = true;
}

// Loop through shipping items
foreach ( $items as $item ) {
    $item->set_method_title( __("Amazon shipping rate") );
    $item->set_method_id( "amazon_flat_rate:17" ); // set an existing Shipping method rate ID
    $item->set_total( $cost ); // (optional)

    $item->calculate_taxes( $calculate_tax_for ); // Calculate taxes

    if( isset($new_item) && $new_item ) {
        $order->add_item( $item );
    } else {
        $item->save()
    }
}
$order->calculate_totals();
$order->save();

$order_id = 2343;
$order    = wc_get_order($order_id);
$items    = (array) $order->get_items('shipping');

if ( sizeof( $items ) > 0 ) {
    // Loop through shipping items
    foreach ( $items as $item_id => $item ) {
        $order->remove_item( $item_id );
    }
    $order->calculate_totals();
    $order->save();
}