Ground wires are often just bare solid wire. Shielded wire certainly wouldn't hurt but you usually ground the shield anyway which makes it kind of pointless. On a hollow-body the ground wire is often insulated, though. My guess being that this allows easier to bend stranded wire to be used so that it's easier to maneuver the pots while trying to install them.
Re: pipe cleaners, sounds good to me! Just be careful because if they're like the ones I have here, pulling on them against the holes could lead to abrasion on the side of the hole. Be careful and it shouldn't be an issue. I've used tubing, dental floss, and my favorite - a specially twisted old coat hanger piece.