The factory coax on those Volvos runs out through the mirror brackets to the antenna mount at the top of the mirror. Your bird perch mount is screwed in right against the door so some coax is going to be exposed on the truck.
You really only have two options here without drilling holes.
Option one: Cut the PL259 connectors off of one end of your coax, and the factory coax. Place the two freshly cut coax pieces end to end and use electrical tape to tape them together. Then pull the old coax out of the truck. This will pull the new coax through following the path the old coax followed.
It's never going to be as easy as it sounds however as there will be lots of things to bind the coax to the truck, and make it difficult to pull. You will most likely end up removing the mirror cover, and a few interior panels to make the coax easy to pull through.
Option two: Run the coax straight out to the bird perch mount through the open door. Basically, pinch it in the door like you are trying to avoid.
Most people who eliminate the factory cophased antennas run their single antenna on the left side of the truck. I would place the bird perch on the passenger side door and run it out through there, less opening and closing of that door.
The more aerodynamic these trucks become, the bigger a pain in the ass it becomes to mount antennas. A W-900 still has a rubber grommet the coax passes through and out to the mirror. Its about a 5 min job on that truck, but I feel the era of the W-900 and the 379/389 is coming to an end.