The easiest way to upgrade a WordPress site from version 2.9.2 to 4.9.8.

I have a WordPress site running under version 2.9.2 of WordPress. I have succeded in making a copy on my local computer running under WordPress version 4.9.8 by installing an empty site and using export and import to fill it up..

I would now like to upgrade the online site from 2.9.2 to 4.9.8.

What would be the easiest way to do that? I don’t want the online site to be down for longer than necessary.

As a supplementary question, could I install 4.9.8 on an alternative sub-domain on the server and make it access the mySQL database that the 2.9.2 version uses? If that worked, I could switch the domain pointers later.

I am aware that the current version of WordPress is 5.5.1.