How to properly style hika and remove inline style

You can override the front end CSS file via the configuration indeed.
You don't need to set it to none. Directly change the code in it and save the file and the configuration and that will use a custom CSS with your modifications.

The CSS added to the head is added based on the options of your modules and menus. For example, if you set a blue background color, it will add the corresponding CSS for that menu/module.
It has to be dynamic.
If you don't want it and want to have your own CSS, you can go in the table hikashop_config via phpmyadmin and add a new entry with the namekey no_css_header and the value 1

For the inline CSS to calculate width, that depends on the number of columns that you configure in the menu/module. If you remove it, it won't be able to display the categories on several columns with the list display.

Edit it. That will create a CSS override file. Exactly what you want.