First of all we search throuhg all the files for the widget class that adds the "product_details.css" file.
It is \XLite\Module\CDev\ProductOptions\View\Product. Here is it:
https://github.com/litecommerce/core/blob/1.0-master/src/classes/XLite/Module/CDev/ProductOptions/View/Product.php
As you see the class "decorates" \XLite\View\Product\Details\Customer\ACustomer class. "Decoration" means that after the cache rebuild process there will be no ProductOptions\View\Product class anymore, but the changes will be included into the class being decorated. That's why if you want to "decorate" it further, you should extend the base \XLite\View\Product\Details\Customer\ACustomer class, not the ProductOptions\View\Product one.
So, we create a module, specify "Cdev\ProductOptions" in its dependencies, add a new class that decorates the \XLite\View\Product\Details\Customer\ACustomer class and declare getCSSFiles() method that parses the array returned by parent::getCSSFiles() and removes "product_class.css" from the list.