I’m afraid I don’t understand.
The tabs are not in the results; they’re different scopes / methods of searching. If you remove the tabs for system, shadow, and filter, then you only have the standard tab… and you don’t need a “tab” at all if there’s only one of them… and then you have something that looks almost identical to the $:/core/ui/SideBarSegments/search
(although there’s still a difference, which is that advanced search shows results within the tiddler body, rather than as a dropdown).
You may be interested in a readOnly plugin, if you have the general need to reduce clutter for visitors who are focused on a theme that has nothing to do with TiddlyWiki.
One such discussion is here: Simple solution for an online read-only TW
There may be others, more recent. At any rate, there are tons of interface elements that I suppress when the wiki is loaded over the web, but which show when I’m editing locally, or when I have an active connection to tiddlyhost.
At any rate, you could certainly edit the advanced-search button (in the sidebar, which is the $:/core/ui/Buttons/advanced-search tiddler) to open up the standard search directly (the part that displays under the tab “standard”), rather than the set of tabs in the advanced search:
$:/core/ui/AdvancedSearch/Standard
Perhaps you’d still want to keep the keyboard shortcut to open up the full Advanced Search, for wiki editing purposes…