When I splice wires which are that important I use an old military techinque:

• Make a clean cut of each wire end.
• Strip back about 1/2" of insulation on each side.
• Slide an oversize size shrink tube on onte of the wires and out if harm's way.
• Do the same for the other side but use larger shrink tube.
• Fray the ends of the wires slightly.
• Mate the frayed ends together, interlocking them.
• Solder the frayed ends together (remember, heat the wire, let the wire melt the solder).
• Slice the smaller of the shrink tube over the soldered joint.
• Heat the shrink tube to isulate the solder joint.
• Repeat using the larger shrink tube.

This makes a good mechanical and electrical connection. It can be a bit tricky not to make the solder joint too big, and not to ruin the existing wire insulation.

Ethan