Not sure on the type of boat or setup but I've rigged a ton of them in my days. Some boats have removable boxes where the steering cables and wires go through. Some of them have all aluminum boxes that will not come apart. I recomment the pull string method as mentioned above. When pulling the old wire out, make sure to pull a string through with it. The most invaluable tool I use is a fish tape. You can push this through your wire chase, tap your new wires to it, then pull it back through.
Yes, I've had to cut a wire or two in my days from an old transducer but that was after all options had been exhausted.
I have OCD "Obsessive Crappie Disorder"