The original handle wrap looked like this:
Removing the original wrap:
After that I removed the leather cover of the handle to expose the holes for fixing the new paracord. First I drove the paracord through the hole close to the end of the handle, then keeping equal lengths each side I used the other hole close to the blade as you can see in the pictures:
I fixed the leather on the handle with double sided adhesive tape:
Then I clamped the knife in a vice and pulled both of the strings to the same side. After that I started the wrapping putting one twist per side while keeping the strings thight:
It sounds a bit confusing but it's easier to do than to describe. When I reached the end of the handle I made a simple knot and melted the end of the cords. It's definitely not the most elegant method, but it works well.
The end result:
Let me know what you think about the result.