Clients that use the API won't see a difference. They get raw content output and don't rely on skin features at all.
You can simulate that kind of response with the render query parameter:
https://en.wikipedia.org/wiki/59th_Academy_Awards?action=ren...
but clients probably use more specific API endpoints, like fetching the HTML:
https://en.wikipedia.org/w/api.php?format=json&action=query&...
or plain text:
https://en.wikipedia.org/w/api.php?format=json&action=query&...