Transfer wordpress files

I have cloned our work website https://www.schoolfurnitureoffers.com so I can work on a new design on my own server but using all the existing content.

How do u transfer the new design to the domain server above but only the design, theme, amends etc without overwriting the woocommerce clients, online purchases, etc that have been done while I have been working on the new site.

Here is the new design I am working on https://s579117298.websitehome.co.uk/