First of all, you need to create a custom tool geometry as single mesh - i.e. you can model it in Rhino, mesh it, and then join the meshes.
At the robot, every tool is defined by XYZABC values defining the offset from the flange. In your case, with the tool 102mm away from the robot's flange it would be XYZ would be 0/0/102. If you set ABC to 0/-90/0 and define the robot's position via a plane, the plane's Y-axis will be the wire and its Z-axis will face towards the robot's flange.
Of course you also have to set the same tool values at the robot itself (Start-Up/Calibrate Tool/Numeric Input, see p.109 of the KUKA KSS 8.2 manual)
The tricky thing with hotwirecutting is defining the best direction from where the robot holds the hot wire to optimize reachability.
I've attached an example-file to this post.
One more thing: 102mm seems like a very small wirecutter for a KR60HA - are you sure about that? If it's 102cm then you have to use 0/0/1020 for XYZ instead. In the example I used an Agilus with a tiny wirecutter :)
P.S.: I'm on the train at the moment and couldn't watch the video - will do so ASAP.