Jon,
I think you are trying to fish the wire across from port to starboard for the cabin interior lights? If so, it is not an easy task. Removing that piece of teak trim will only lead you to a solid fiberglass side of the beam. The picture I have included is after I cut the bottom from the beam to repair my collapsed compression post support. Look at the left side (which is aft) of the wood up in there and you will see some wires. (Not the ones in the tube down the middle of the wood, that's for the radio antenna on the mast). There is space for both the 110V 12-3 conductors to supply AC voltage to the outlets on the starboard side. You should see a blue and a black pair of wires that supply the lights on the same starboard side. Fishing through might be difficult as I don't know exactly the route the blue and black pair take from the port side into that beam. You can try and remove the forward most eyeball light on both sides and tug on the wires to see if it moves on the opposite side of the cabin. If so, you may have to cut the wire on one side, tie your fish tape or a string and try to pull it across. Then you can fish new wire back with that pull string. The second location of the wire path might be after taking down the overhead panels that the big round lights are hung from. If all else fails, you may have to drill holes to facilitate fishing new wire and install plastic caps to hide them.
Let us know if that is the wire you are trying to replace, or is it something coming down from the mast that you are trying to route back to power.
Allan