Since I posted I've been doing some research. The Lumia 822 uses a Micro SIM and the HTC One uses a NANO sim so they will not be compatible.
However. I noticed that phone that I purchased (from eBay) included a SIM. I am guessing it was the one they used when they had the phone on Verizon's network. I've also got a Verizon NANO SIM that came out of an iPhone, again, once used, but no longer.
So, the question is:
Can SIMs that were previously used for service be re-used or do I need to get a new one? I've heard various stories that some Verizon outlets charge for SIMS and some do not. I'm hoping that I can do this without any additional expense. My preference would be to use one of the 2 SIMs that I already have so knowing whether I can do that will be important.