I had not considered this until someone recently asked about using Integrity to do the job.
Yes, in principle you can export your bookmarks from Safari or Firefox as a .html file and ask Integrity, Integrity Plus, Pro and Scrutiny to check all of the links it contains.
The only issue is that the free Integrity, and App Store versions of Integrity Plus and Integrity Pro are 'sandboxed', meaning that for security reasons, they generally only have access to local files within their own 'container'. Apple insists on this measure for apps distributed via their App Store.
For this reason, those versions of those apps will not be able to fully crawl a website stored locally (some people like to do this, although there are some advantages if you crawl via a web server, even via the apache server included with MacOS).
However, here we're only talking about parsing a single html file for links, and testing those.
A sandboxed app can access any file that you have chosen via an open or save dialog.
So all you need to do is to use File > Open to choose your bookmarks.html file rather than typing its name or dragging it to the starting url field. (Remember 'check this page only' to ensure that you only check the links on the bookmarks file and the app doesn't try to follow all of them.)