If you want to do a really neat job of joining the two wires here is how to go about it (this is how I do it when I am extending wiring harnesses to hide to wiring in an engine bay etc).
You need two sizes of heat shrink, one big enough for each wire, and one big enough for the bundle of wires (in your case it will only be 2 wires).
Do not cut the wires right near each other as when you do your joins there will be a big ugly bulge in the harness, you need to stagger the joins by about 50mm.
1. Cut your wires and temporarly hook them up to see if it is working.
2. slip a peice of the large shrink wrap over all the wires (make sure it is long enough to cover all the joins + 50mm at each end.
3. put a small peice on each wire.
4. solder the wires togeter
5. shrink the small bits over each wire
6. slip the large peice over the other joins and shrik it
If you have done it well then you will have a very neat join that is water tight with a long gentle bulge instead of a big sharp lump.
Now for the cheat / cheapest method
Get a bit of shrink wrap big enough for both wires stagger the joins by 50mm or so, doing this means that the bare wires cant touch as thay will be 50mm apart. Shrink one peice of heat shrink over both wires, presto. Not as professional as the first method but quick, neat and less stuffing around.
