A swelling element on a packer has a trough formed on a longitudinal axis. The control line or cable or conduit that needs to run along the string where the packer is mounted is first wrapped in a preferably non-swelling underlayment that can be a loose scroll or have its seam sealed. A swelling cover is placed over the underlayment using a seam that can be longitudinal or spiral to allow rapid deployment. The covering assembly for the control line or conduit is placed in the slot of the swelling element of the packer. The line or cable continues out opposed ends and can be secured to the tubular string with clamps. In an alternative embodiment the control line is covered with a swelling material and forced into a groove that runs the length of the packer swelling element.