Scroll down the page to the Specifications and see if the measurements match the flat section of your threaded spindle ends.
The flat end in your photo doesn't look too bad, but sometimes these can get "oval shaped" from wear and tear during the up-and-down winding over the years.
If the CaravansPlus winder suits your needs, I'd buy two of them. Keep one as a manual winder, and cut the end of the second one to have the socket and a few inches of rod attached. That way you can insert the socket/rod into a cordless drill and do similar to what Mustang does with his set-up.