If you want to avoid creating a subdomain for your new WordPress website, and have a live website on a another host, and want to preview your new website on your new host without changing your local HOSTS file (and explain your client how to do it, which can be challenging in itself), you can try one of these 2 services:
https://hosts.cx/
https://skipdns.link/
They allow to get a temporary URL. You simply input the actual domain name of the site, the IP of the new host, and it will give you a URL to test out.
Note: Depending on your website, it might not work, and the rendering might not be perfect, especially the javascript portion.
