There is no way to duplicate a product without the custom options (without overriding the product model), but you can duplicate the product and remove the custom options after that.
$clone = $product->duplicate();
//all your additional code here
//then delete the options
$options = $clone->getOptionInstance()->getProductOptionCollection($clone);//get all the options
foreach ($options as $option){//loop through the options
$option->delete();//delete each option
}