You can't achieve that in config, since text formats are configured per field instance, but not as granular as for to get to the node level.
You'll need too implement a hook_form_alter(), and then check the url to find out if you want to allow the format or not. Something like this:
function mymodule_form_alter($form, &$form_state, $form_id) {
if ($form_id == 'node_type_form_to_alter' && (current_path() == 'node/%nid/edit')) {
// Enforce desired text_format here, by altering $form array.
}
}
That's what I would do for that case. You can take the opposite approach, and implement the same form_alter, but instead of enforcing it on a particular URL, just making sure that it's not available unless the url is the one you want to target.
Hope it helps.
EDIT: To enforce the format, you need to find the field you want to alter, inside the $form array. Wysiwyg fields use the 'text_format' when declaring the field through Form API (example here).
So, you have to find the desired field, and change the '#format' property (as in the example), to the machine name of the text format you want to use. Also, you'll see a 'format' propery in the element array. You might want to change that too if you want avoid certain formats from appearing in the dropdown widget.
I recommend you use xdebug to see the structure of the $form variable inside the hook_form_alter() implementation. Alternatively, enable the devel module, and stick a "dpm($form);" in that function, to render the structure on screen when visiting the node form.