Can I use two Apple Watches with my iPhone?

I have my old watch, that doesn’t hold a charge for the whole day anymore, so I decided to get a new one. However, I would like to use my old watch to track my sleep at night. It doesn’t need to have cell, it can use Wi-Fi to let me know my sleep patterns. But I need to connect my new watch to my cell service, and don’t want to have to erase everything on my old watch. I am on Verizon, does anyone know if this is possible? Or how to accomplish it?

[Re-Titled by Moderator]