You'll need to make a few registry changes if you want WDS to stop flaunting its existence. The keys you need to change are below, or you can copy+paste the code snippet, or download a registry file (restore_full_windows_classic_search.reg).
Remove the WINKEY+F binding
HKEY_CURRENT_USER\Software\Microsoft\Windows Desktop Search\DB
UseWinKey = DWORD:0
Don't the WDS Pane if you hit CTRL+F in an Explorer window
HKEY_CURRENT_USER\Software\Microsoft\Windows Desktop Search\DS
ShowStartSearchBand = DWORD:0
Use the Classic Search pane, not the Search Assistant dog
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\CabinetState
Use Search Asst = DWORD:0