Thanks for all the input. I just picked this up at Best Buy (normally $19.99, on sale for $6.99):
http://www.monstercable.com/productdisplay.asp?pin=5246
It's precisely what I want, with the exception that the microphone cable is only 3 feet long. I'll see what I can do to get it to a useable position in my car.
Would it be difficult to cut it and splice in a longer length of cable to route it where I want it on the visor? What type of wire would I use?
Thanks!