You probably couldn't use the old wire to pull a new one since I am pretty sure the original group of wires is bundled together with tape or ties.
Follow you motor control cables and they will lead you to the opening in the rigging tube which may be a 3 inch or so pipe. Try snaking that. If not, find the other end of the rigging tube. You may need to remove panels or possibly a built-in storage shelf/drawer/etc to get to the opening. Try snaking from that end. One way or the other you will get a snake through. After the snake, pull a drag rope along with the new wires. There may be a tube from aft to the helm area and either an open path or a cross tube to get to the mid bilge area.
It is very possible that you can't easily see the opening of the rigging tube aft by looking in the bilge. Try a mirror or try holding your phone in the bilge towards the side and aiming forward (or aft is looking from the helm end) and take pictures, The tube is there somewhere. As I mentioned, the motor control cables feed into it.
If your snake has a straight cut end, it may not pass the plumbing and wiring without getting stuck. heat the tape end and put a loop in it.
Also tray feeding the snake into different areas of the tube, like up top, instead of on the bottom.
Many folks have better results using the newer fiberglass electrician tapes which are plastic rods that can be connected to each other to make a longer snake. The advantage is that they can flex but also will run straight in a straight pipe unlike the metal tapes that tend to take to curl
Here is an example
Boeray 11' Fiberglass Running Electrical Wire Cable Pulling Fish Tape Kit with 5 Different Attachments and Fish Tape Tool in a Carrying Case - - Amazon.com
www.amazon.com