[Aussie Mike]

I've cut and resoldered wires many times and it can be done reliably. I use a small piece of heat shrink tube over the join.

Cut the wire and strip back about 1cm of each. Make sure the copper is nice and clean or it won't solder well.

Slip a length of heat shrink tube over one of the wires and slide it back away from where the solder joint is or it will shrink before you need it. I sometimes use 2 pieces and shrink one over the joint and then slide the next along and shrink it over the first.

Twist the wires together inline, not at a T to the original wires. This makes for a neater looking join that can be almost invisible one heatshrinked.

Use some good quality electronics flux cored solder and a soldering iron. I don't like using a torch on electrical soldering as it makes a mess of the insulation.

Heat the joint with the tinned tip of the iron. Once it's heated the joint enough feed the solder into the intersection of the tip and the joint. The solder should wick into the joint. If it doesn't then you haven't tinned your iron properly or applied enough heat. Once the solder wicks into the joint you can apply the solder directly to the joint. Don't use too much though as you don't want the solder wicking along the wire and making it rigid. You don't want a big blob of solder blob at the joint, just enough that the copper color dissapears but you can still just see the shape of the wire strands.

Remove the heat and hold the wire till the solder hardens. This is the mistake often made that when the iron is removed the joint moves around and you end up with a dry joint.

Slide the heat shrink tube along and shrink it down with a heat gun. make sure you have about a cm over each side of the joint.

Cheers