You can use:
dpkg -l | grep scope
to list all scopes installed on your computer.
For 13.10, all you really need is: libunity-scopes-json-def-desktop, unity-scope-home, unity-scopes-master-default, unity-scopes-runner.
You can safely uninstall all the other scopes and still have a working dash that will only search installed applications.
You should probably be interested to know what "intrusive" lens application exist as well.
dpkg -l | grep lens
will list all installed lens applicaions
For 13.10, all you really need is: unity-lens-applications and maybe unity-lens-files as well.
Again, you can safely uninstall all the other lens applications and still have a working dash that will search installed applications.
To remove those applications, copy/paste this entire command into an open terminal.
sudo apt-get purge unity-lens-friends unity-scope-audacious unity-scope-chromiumbookmarks unity-scope-clementine unity-scope-colourlovers unity-scope-devhelp unity-scope-firefoxbookmarks unity-scope-gdrive unity-scope-gmusicbrowser unity-scope-gourmet unity-scope-guayadeque unity-scope-manpages unity-scope-musicstores unity-scope-musique unity-scope-openclipart unity-scope-texdoc unity-scope-tomboy unity-scope-video-remote unity-scope-virtualbox unity-scope-yelp unity-scope-zotero unity-lens-friends unity-lens-music unity-lens-photos unity-lens-video
Always pay attention to the following prompts to ensure you do not uninstall something you wish to keep on your system in the process.
I just use nautilus to search files but I'm sure you'll get the just of what you need to do here. Also, you still have to change privacy settings to "do not include online results" to maintain your privacy.