There are 2 types of search screens in Total launcher, which are open by the launcher actions: App search and Contact search.
App search screen
You should know first how the launcher action (ex: App search) works. When you invoke the launcher action, the launcher tries to search a most top app drawer widget. If the launcher has found an app drawer widget, it would be used to show the search results. Otherwise, it opens the built-in window with an app drawer in the screenshot. As you guess out now, since you cannot change the design of the built-in window, you should make a your own window instead. Here's the steps for the solution.
1. make a new window.
2. put an app drawer widget onto it.
3. customize the design of the window and the widget.
4. set "Action on open" to the launcher action (App search) in the window options.
5. open the window for your own app search screen.
You can make your own contact search screen in the same way.
Thanks.