WordPress Multisite Problem

Hello, I have a problem with a WordPress multisite network. My client asked me to restyle a website and I added a new WP site inside my client0s network. I thought to develop the site directly on their system and once completed, to replace it with the site that is currently on the root of the domain. The new site that I developed is available at http://www.new.myartego.com and I should make sure to disable the old site currently on the domain http://www.myartego.com and replace it with the one just made. Within the newtwork there are also other sites that should not be affected by this operation.

I’m having several problems to perform this operation because the guides so far found were not helpful. what I should do is simply disable the main site of the network and replace it with the one just created without damaging the other sites on the network. Could you kindly give me a hand?