Verizon does contract with a company to do this for you. It's called CBW Productions Inc. and their Verizon section can be found here: www.cbwproductions.com/vwclientsorder.html
Your best option for the 1 voicemail is to pay $5 and they will send it to you as a .mp3 or .wav file via email.
And DigitalTony had this to say a couple of weeks ago:
I used a differen't service to save my voicemails before activating my new iPhone.
I didn't know about CBW, but SaveMyVM did a great job and they
delivered my messages within 2 hours.
Check out both of them and see which will work best for you....
**If you want to save future voicemail messages, use either Visual Voice Mail (a fee based service from Verizon) or YouMail or Google Voice; they all allow you to listen to and SAVE voice messages on your computer. You Mail and Google Voice are free.