Static HTML to WordPress migration

I would agree with the commenter – develop your WordPress version locally using something like MAMP (if Mac) or WAMP (windows). In that way, there would be no disruption to your existing site until you are satisfied and ready to upload the WordPress version.

When you are ready to upload, I would (personally) clear out the whole of the static site (assuming you have backups) and create a fresh installation of wordpress in the root of the site, then upload your theme files, import your database etc.