Just an update – I have managed to do this manually and it works well.
For the benefit of others, I first created a new widget (/wp-admin/widgets.php) called 404 Search and then added the Xstore search widget to it, then saved this.
Then I created a new static block (/wp-admin/edit.php?post_type=staticblocks) and created my page layout, then added the widget into the correct place using the WPBakery Widgetised Sidebar element.
Copy the new static block code (i.e. [block id=”6400″] ) and paste it in Xstore theme options -> 404 page in the content box.
My 404 is now fully customised exactly how I want it and it uses the search option I wanted too.
Very easy once I sat and thought about it. 🙂