Hi Eric
You probably don't have any issues with the wire. Most people run some sort of a non conductive connector to their weight. It won't matter if it is plastic, rubber, or twine, as non of them are conductive. I expect that your downriggers are isolated from any boat metals, so there won't be any interaction there. The only thing that might give you wire voltage is if you have a lot of brass markers crimped on, or other metals connected, but even that should not be an issue. Saying that, positive voltage is your friend, and we want some down there.
I suspect that, if you are having issues, it is probably originating from the boat. What method are you using for testing your boat, and what are you seeing on the meter? Also,what motor/kicker setup are you using? Al