Your comments

I don't think it's a good idea.

Pros

  • Universal, works for all browsers.
Cons
  • We have to run an additional process/service which will function as the proxy server.
  • We will process all the system traffic, only to handle a couple of websites which are being visited about once a month.
  • We have to open a port on the system, which might conflict with other software.

I'm not very experienced with proxy servers, so I may be wrong, but that's how I see it.
Coverity Scan is a service by which Coverity provides the results of analysis on open source coding projects to open source code developers that have registered their products with Coverity Scan.
(from the FAQ)

Unchecky is not an open source project.
Coverity Scan is a service by which Coverity provides the results of analysis on open source coding projects to open source code developers that have registered their products with Coverity Scan.

Unchecky is not an open source project.
Looks great, well done!
Also check out this, by JohnKiller:
https://github.com/RaMMicHaeL/unchecky-for-chrome
The problem with a userscript is that unlike a browser extension, it can't be automatically installed by Unchecky, as it needs an additional extension such as Greasemonkey.