I have unlimited data with Verizon also and have used the exact same SIM card for the last 3-4 years, just moving it from iPhone to iPhone. Just don't turn on the new device until you put in your activated SIM. And destroy the new SIM card to be safe.
Yup, exactlyI guess this is what I was after...so, put my old/current SIM in the new phone and don't use the SIM that comes with my new 6S?