Does anyone know how to wire up the fog lights to turn on without having the low beams on? possibly use another fuse?

Either get the stick that actually has the knob for fogs and wire it to that, or wire them to a completely separate custom switch.

From the headlight switch there should be two different power wires. From the factory 1 of them runs to the fog switch so that it will only turn on from the headlights. What you need to do is figure out (from a wiring diagram, sorry no link) which wire gives power from the running lights so you don't have to have the headlights on.

Or just find a wire that's always hot when the key is on and wire that to the fog switch.