How do I remove only shopping searches?

You can't remove the Unity Shopping Lens in Ubuntu 13.10 because there's no Shopping lens. Ubuntu 13.10 comes with a feature called Unity Smart Scopes (or "100 scopes") which uses a huge list of scopes to display results in Dash and among these, there are some used for shopping. So if you don't want shopping suggestions in Dash, you must disable these shopping scopes (see below). Unity Dash without shopping suggestions

How to disable Unity Dash plugins (scopes) in Ubuntu 13.10

To disable a Dash plugin (scope) in Ubuntu 13.10 Saucy Salamander:

• open Dash,
• go to the Applications lens (either do it manually using your mouse or use the Super + A keyboard shortcut),
• click "Filter results" on the right and under "Type",
• select "Dash plugins".

All the Dash search plugins (scopes) should be listed.

To disable a plugin, click on it and then click the "Disable" button. Later on you can enable them back in the same way.

Disable the Amazon / shopping suggestions Unity Dash scopes

If you don't want shopping suggestions in Dash, disable the following scopes (by using the instructions above): Amazon, Ebay, Music Store, Popular Tracks Online, Skimlinks, Ubuntu One Music Search and Ubuntu Shop.

To disable all these shopping Dash plugins/scopes from the command line, use the following command

 gsettings set com.canonical.Unity.Lenses disabled-scopes "['more_suggestions-amazon.scope', 'more_suggestions-u1ms.scope', 'more_suggestions-populartracks.scope', 'music-musicstore.scope', 'more_suggestions-ebay.scope', 'more_suggestions-ubuntushop.scope', 'more_suggestions-skimlinks.scope']"

There's now a GUI for doing this.

Open "System Settings" (type that in the Dash). Then go to "Security and Privacy". Then "Search". Then set the "include on-line search results" to off.

Disclaimer: It seems likely that this prevents the system from phoning home with everything typed in to Dash, but I'm not positive of this.