How to restructure the mega menu and side filters on our live shop?

Hello Shopify community & Gurus

We need advice on the safest, best practice on how to restructure the mega menu and side filters on our live site www.strompe.no
We are using the Turbo theme from Out Of The Sandbox, and have installed their Theme Updater App.
Unfortunately, the Theme Updater App is unable to update our theme and carry over the with the current customizations that has been made… (we are currently using 4.53)

We made a duplicate copy of our current live site, and manage to change around colors and fonts, etc. But we really need to rearrange the navigation and menu structure, and Shopify tells us this is not possible.
We might some days as we restructure/rename the menus, filters, and tags, etc. until we push the “save” button.
We find it very scary to work on the live shop without pushing “save”.
Can you offer a solution to the above?

Best regards Geraldy, STRØMPE
www.strompe.no