When performing repeated edits edits on a site, is it possible to force a cache of the site that results in new edits being displayed rather than having to delete my browsing history to see the new edits?
Yes.
By adding a query string (staring with a question mark) to the end of the address it will force the browser to load it anew.
For example, you can use "v" for version, e.g., http://example.com/?v=1
Then when loading a new version and you want to see uncached in the same browser, increment the version number in the URL, e.g., http:/example.com/?v=2
That's typically just for internal use related to re-viewing the content. It usually isn't necessary (or helpful) to share those URLs because each one of those gets cached.