Sure. Speaker wire should work for a CP, it's not high current or voltages.
Happ sells spools of wire. Radio Shack, Fry's Electronics, Incredible Universe, you might check if there are any local electronics supply stores in your area. Note I said "electronic" and not "electrical".
Maybe a local TV repair shop can sell you some, or at least tell you where to get it.
EDIT- Also, be sure you are getting "stranded" and not "solid" conductor wire. Especially if the harness will have to flex anywhere, like when you open the CP.