Unfortunately you'll probably need to cut the BNC end off the connector, fish your cable, then re-install a new BNC connector.
You can get BNC connectors at Radio Shack or many places on line. They are quite simple to install. You can get either "Crimp on" or "Twist on" styles. If you have access to the appropriate size crimping tool, crimp type is your best option. If not, then the twist type are okay (but not great).
Usually I get three or four of them as they are inexpensive. I get the extras because sometimes I'll lose one of the components in the bag or not do the best crimp job and end up re-doing it (or at least when I first started doing this).
There are several rubber grommets in the fire wall, usually near the steering column. An ice-pick, carefully used, can create an opening through which you can pass the cable.