UPDATE: Possible lead to finding the demo.
A large amount of demos were leaked and illegally sold online under the name "A-ha Most Wanted - 79 Demos Pack". This contains an alternate mix of the final demo of Take On Me (seen on Swing Of Things and deluxe edition of Hunting High And Low) and an instrumental version. I'm pretty sure this is what we're after. However, I can only find one track from this, being an alternate version of an a-ha demo called "All the Planes That Come in on the Quiet", the most noticeable difference is Morten Harket, a-ha lead singer, saying "Pokker ta den her sangen" (Damn this song) at the beginning. Here's that if you're interested: <a rel="nofollow" class="external free" href="https://www.youtube.com/watch?v=BCiCAi1xDho">https://www.youtube.com/watch?v=BCiCAi1xDho</a>. Hope more will be found of this, as it seems to be our best hope to find it.