The Tab key should switch between the "search by name" mode (which is shown in the screen shot) and the shortcut key mode (where you press a letter or number to paste the clipping).
If this isn't working for you, please do the following:
1. Invoke the Clippings keyboard paste dialog (default keys ALT+CTRL+Y)
2. Right-click on the dialog and select Inspect Element from the context menu. This will open the Developer Tools
3. Click on the Console tab
4. With the Developer Tools open, go back to the keyboard paste dialog and try pressing the TAB key
5. Check the Console tab in the Developer Tools window for any errors/messages that may appear.  Copy it and paste them here so that I can review it.