I've swapped twice, but both times in the Microsoft Store. I don't think they did anything other than swap out the SIM, AFAIK from Verizon's perspective. Of course they scanned the barcode and gave me a new receipt (with the new IMEI number on the receipt), but they didn't pull out their special "Verizon" laptop to make any changes to my account, at least not that I saw. If I was getting a phone in the mail, I think the first thing I'd do is swap out the SIM and do the startup process, and see if that's all it takes. Worst thing that can happen that way is that it says there's no signal available.
Be ready to connect to WiFi as soon as you get to the start screen if you're doing a restore, because otherwise you could burn through a lot of your data plan as it downloads and installs apps. Last time I did this it took 1.7GB of WiFi (looking at DataSense afterward).