Well, if you run all new wires, and put a fuse in there it should be fine...
with a relay you have 4 things... in power, out power, switch, and ground. I think you know what the ground does, the in power will be power from battery/selenoid, out power will go to fog lights, and the switch will be a wire run into the car onto one side of a switch, then go to the fuse box to a fuse that has power when the car is on. Then when you flip the switch on the fog lights will be on, off when you flip it the other way. That way it will be independent of any other lighting devide and you should have no problems...