Hi green!
I can tell you, for sure, that African tribes of the Dogon and Pygmies still use that type of axe.
Howewer, I'm writing my thesis about experimental archaeology, and a huge help to this discipline comes from anthropology: I'm going to study African tribes that are still using our Bronze/Iron Age technology and tools, so I'll report anything of interest

Your link is very interesting, and in this page
http://www.ancienttouch.com/neolithic_and_bronze_age__bronze.htm it reports as "celt axes" these that were mounted in the L shaped handle.
Being more recent than Otzi's, these "celt axes" were casted with a hole that had to be filled with the branch; in Italy, we call them "ascia a cartoccio", and are typical of my ancestor's civilization, the Piceni.
They were common between both the left and the right side of the Adriatic, testifying many links between the Piceni and the ancient Albanians - which produces many interesting questions about the Piceni's origins.
In this other page
http://www.ancienttouch.com/bronze_age%20axes,%20adzes.htm, you can see how the type of axe you're willing to recreate comes from Near and Middle East

Greetings,
Mauro.