Running cable through cavity

Hey i have a curved cavity that i want to run a cable through. I tried creating the path for the cable with a 3D sketch and then sweep my cable along this path but because the cable is only slightly smaller than the channel it is running through, it keeps intersecting the cavity walls.

Is there any way to run a cable or tube through a channel without having it touch the walls? I have attached my solidworks file, sweep 8 is the cable i am trying to create.

SolidworksParts And Features