How do I customize Product Search results?

The built-in search results widget for WooCommerce gives far more relevant results than the third-party search plugins out there (I’ve tried the two most popular ones and they are both pretty terrible) but I want to change a couple of things on the search results page. The WooCommerce Product Search plugin that WooCommerce offers for sale doesn’t have any impact on the search results page itself so that’s no help either.

In particular, I would like the images to be smaller and, more importantly, that it would show a short excerpt of the Product Short Description for each item instead of the entire Short Description, like say, limit it to the title and first 50 words. Can those things be done through adding some code to the functions.php of my child theme?