Search Page modification

This may seem weird, but right now when you use the search box on my site it takes you to the search results page. On that page it has the post title and a little summary and a read more button. What I would like is to delete the read more button AND get rid of the link from the title of the post/page. Basically, I do not want users to get to those pages or posts from the search results page but I do want them to see the title and summary. I know it’s weird just let me know if this is possible!