Intention
I used solution from lemon, but wanted some more control over the tube thickness. So they could stay the same thickness after displacement.
Using the skin modifier
At first decimate the geometry of the tubes down to one single line with multiple verteciesvertex. I deactiveddeactivated the Viewportviewport display of all the previos modiefiersprevious modifiers for these Stepssteps.
Added a skinSkin modifier
and scaledScaled the verteciesvertex with STRG+ACtrl + A to fit the original shape
toTo make up for the lost geometry I added a SubDiv ModifierSubDiv modifier underneath the skin.
To fix the resulting sharp looking tubes. I added another subDiv infrontSubDiv in front of the skinSkin modifier.
DISCLAIMER: I would have put this in the commonts of lemon, if had enough rep.