The way I got to that was by following Chipp Walter tutorial on solids: https://www.youtube.com/watch?v=jQl-0waABAM

I had some minor changes that was the following: Instead of using a closed curve and thereby slicing a piece of the box out I just separated the piece. Afterwards I took it out and shelled it to remove everything but the tube like outline:

First I booleaned the box with the two open curves.



Result seen in perspective:




Part taken out but before using shell (not needed to show the point).



So I can't see any other way to do what I want than having the center points afterwards some how. I can't get the centerline from the curves because the curves doent go in depth and the box has fillets so there is also some bending after final results.