Can bike/motor brake (and/or) gear shift cables used as a conductor
I should wait for the answers to the resistance measured and current needs but I believe its safe to assume a thin stainless steel braided cable of 4 feet is unlikely to support what you want to do. It has high resistance, aside from the issues about coatings or shorting to its case. Bowden cable is stainless steel cable in 2 or 3 layers meant for mechanical force not electrical properties. For any reasonable lighting needs it will just cause enough voltage drop to make it unusable but unlikely to get hot enough to be unsafe.
If you need a specific color cable and the brake cable's outside is what matches, then get regular wire (stranded more likely to last longer) and use the brake cable's sheath as a conduit.just cut the inner braided cable end off and pull it out. You can then thread the normal wire or wires in. You could also use the bike frame as a conductor but that involves tapping or sanding paint off and has some issues with material (carbon fiber is not going to work. Aluminum would be better etc).