A good article to help convince your client along with the information from Daniele here: 404 Page Best Practices

I hear what you are saying re having the control over the code, I've been coding for more years than I care to remember however I prefer to run sites on Wordpress for a number of reasons such as control over content, navigation is simplified, translation management, hundreds of plug ins and it's written in php so is a standard language.

I always use a child theme and recommend anyone to create one for their theme if the developers has not provided one for you. This is where the real control over a well written theme comes into play. I have full e-commerce sites using woocommerce, optimised using yoast and customised to work and look exactly how I want by me and my team.

I would just say try it, get a decent pre built theme (suggestion only - http://themeforest.net/item/impreza-retina-responsive-wordpress-theme/6434280) to give you some idea what Wordpress and a theme can actually do.

Hi,
It is possible but not advisable due to the way WordPress resolves URLs you can find more information on the subject here: Removing product product-category or shop from the URLs

However some have reported sucess via this article: WooCommerce Easy Permalink Solution