How to temporarily replace Drupal with static HTML pages?
Drupal only kicks in when a file does not exist. So if you create HTML files at the same path where a Drupal page existed, the HTML file will be shown, and Drupal will not be instantiated.

Example: You have a path named /node/4.

If you create a folder in your webroot named 'node', and a file named 4, it will be picked up instead of Drupal being instantiated, even if Drupal exists in the webroot. You may need to do some work to set the headers of the file as text/html though, since there is no file extension on the file to tell the processor that it's an HTML file.