Looks like from the plugin's code...
snapshot = None
snapshot_url = self._settings.global_get(["webcam", "snapshot"])
if snapshot_url is None:
if "http" in snapshot_url:
snapshot_call = requests.get(snapshot_url)
if not snapshot_call:
snapshot = BytesIO(snapshot_call.content)
snapshot = open(snapshot_url.partition('file://'), "rb")
...it just uses whatever's configured in the OctoPrint -> Settings -> Webcam area and runs with that. You might consider swapping the two webcam setups in OctoPrint and then the Discord one will work instead.
But if you need to send to Discord both of the webcams then you'd either need to fork the code to create a second plugin or go ask the author on their repository for a feature request.