This is what I call Mojo wire... It will do what you want it to do
This is a good example of very good wire to use. And it is shielded.
http://www.mojomusicalsupply.com/ite...809&id=2112015
Gauge 22 is bigger than gauge 24 so normally it should have less resistance than gauge 24 wire.
This one is not shielded but is still gauge 22 for the same resistance.
http://www.mojomusicalsupply.com/ite...809&id=2112000
It also looks more vintage. I like the look of some black and some white vintage wire inside a guitar, especially a Tele. And it is a nice wire to work with. I wouldn't even think of doing that to my other non Tele guitars...
Add a vintage style capacitor to that and you will get all kinds of comments when you show the inside of your Tele
http://www.mojomusicalsupply.com/ite...974&id=5162035
Btw, be sure to use a soldering iron that is powerful and hot enough so that it can melt the solder fast enough. That's the secret to work on pickups without damaging them.