Exporting webform information programmatically
You might have to create your own.
It would probably be worth submitting back as a new module too.

All you would have to do is implement hook_menu() to add your menu callback.
In hook menu you can set access arguments to make sure no one case use it unless they have a particular permission.

You can add your own custom permission using hook_permission().

Then the callback function could use webform_get_submissions() to load the submissions for a given webform and return them using drupal_json_output()

You could pass in a webform nid argument either via the url, using something like 'get-webform-submissions-json/%node' as your menu path, which would automatically validate the nid and load the node for you. For more information on that see http://drupal.org/node/224170
You could also just pass it in as a query parameter and use $_GET['nid'] in your callback function, however then you need to validate it yourself.