If you want to trick somebody into thinking a webpage has changed, forget about saving it or extensions. As soon as you type the url into your browser and press enter, any changes are gone.
The only way to pull this off is by doing this:
1) install a webserver to your machine (for instance apache)
2) put the edited homepage file as index.html into apache's root document folder
3) open the hidden file c:\windows\system32\drivers\etc\hosts in notepad and add this line:
127.0.0.1 www.thewebsite.com
Now, when you try to go to www.thewebsite.com, the request is redirected to your computer's apache server, which will then serve your edited file.
The result is indistinguishable from the real thing for a layman.
The only problem with this is that image URLs will also get redirected, so you have to save all the graphics of the site before making the change to the hosts file. Browsers usually let you save a page in its entirety, use that to save all the resources, too, not just the HTML code.