If you already have a better search program and want to disable the one in the Start Menu, here's how to remove it.
Launch the registry editor.
Scroll to HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer
Right-click on the right pane and select New, DWORD Value. Name it NoFind.
Double-click and enter 1 as value. Note: This will also disable the Find under Explorer and won't respond to the F3 key. To restore the Log Off User option, reverse the steps by changing 1 to 0 or delete DWORD value.