There might be out-of-the-box tools for this, especially for wordpress, but my approach would involve writing a teeny bit of code and then either host the tool somewhere or just run it on your computer (since you're the only one interested in the result) to save 100% of the cost.

If I were to build something like this for myself (and I might, sounds like a great idea), I'd use a quirky little Python package called scrapy ("The world's most used open source data extraction framework") and simply go through all the "" tags on your site (I see that pretty much all the information is on a single page which makes things much easier), call the "href" or link/url on it, and see what comes back, creating a list of broken links and logging them for the user to review afterwards.