The idea of using shielded cable is to keep all the noise either inside or outside the shield; it works both ways. Your (potentially) electrically noisy device wiring won't radiate noise into other wiring, and likewise your sensitive low level wiring like headphones won't pick up noise from other wires.
So in general it shouldn't be a problem to run these wires together. Your Flyleds lights definitely won't cause any issues!
Your statement "...and make all connections per directions" is a key point. The directions may be different for each system.