Soldato
That is single core shielded wire I think? And yes I'd say you want it shielded, else you have 2 runs up and one run back all picking up hum.The wires to the 3 way toggle on my LP copy have an inner and outer core/shielding (not sure proper name) with the outer all connected together for grounds
Can it be done with 4 single core wires or does it need to be this 2 core/shielded type?
Pic of the toggle ...
What you can do though is get some standard 4 core pickup wire and just run a single length of it. That is shielded, and has a spare core in case you have any funky wiring ideas. Usually it's just 3 wires/cores in an LP: neck pickup from pot, bridge pickup from pot, and output from switch to jack.