Here is a link to the Burley site that shows the quick release you can use with a 16" or 20" wheel. That way you would need the right Internal Diameter dimension hollow tube welded to your frame and this quick release would secure the wheel to your trailer.
http://www.burley.com/home/bur/page_...20_wheels.html
This way you would not have a whole axle... That's how their trailers have the wheels attached.

If I were you I would write to Burley customer service... I did that for one of my trailers and they were very helpfull! I made one of their older trailers change into a jogger. They might be able to work something out for you.

Hope this helps!