i wasnt referring to the magnet wire, ive come across that, its basically solid copper wire with some enamel. the stuff im talking about is like a cotton thread, it actually feels cottony, and whenever ive tried to solder it it just like burns up and melts away. ive encountered it in a headphone cord and in a phone line.
ckj, just be careful when stripping the cord, as there is multiple conductors in there that need to be worked with seperately. i personally would use an xacto knife or straight razor and score a line aroudn the insulation, then you should be able to bend it back along the line and if it doesnt break through, gently touch the blade to it and it should go right through. then work your way around the wire till its all split and slide off the insulation. depending on the cable, it might just have a couple wires inside the outside insulation, or it might have them with a braided shield around an insulated center conductor. if its the coaxial type, you'll need to pull the braided stuff to the side and strip a length of the center one as well. dont take the center back as far as the shield, this way it will keep from shorting. you could get away with doing it outside of the phones, but its really ugly and can get easilt pulled apart, and since you already have popped them open why not go that distance. the soldering shouldnt be much of a problem once you get used to it, they are relatively big pads and all you really need to do is tin the wire, heat the pad and stick th wire on the pad and remove heat and let cool. iron should only be on the pad for a second or so, if that. with a good contact the solder should melt like almost instantly. then plop on the wire nad you're good. but you will likely find it easier to tie the know in the wire before soldering them down.
are these phones the style that the cord splits off in a Y, or does the cord enter the phones on one side and is carried over to the other side internally?