Wouldn't worry about it. Plenty of people don't have rings for their own reasons. If they ask about it just be honest, it doesn't make you guys any less married.
My husband can't wear his at work - Avionics Mechanic - and since he works that much his ring spends most of the time in his pocket. It's kinda just become the norm that he doesn't have it on. I can't wear mine since having our first child gave way to my Jabba moment and it still doesn't fit. That's how we went to our AOS interview too.
You can get a card in a new name with a NOA1 (in some cases...my wife had to try 3 separate times before they would take it). But you must have at least 14 days of legal status left on the K-1, an EAD, or a green card to apply for the initial card.
I used the USCIS website live chat and the agent told me "Applicants are to appear at the ASC that they are scheduled to appear at on the appointment notice. Biometrics appointments are scheduled to the ASC nearest to the zip code provided on a person’s application. If an applicant is unable to appear at this location on their scheduled date, but can travel to another ASC for their appointment, then they may do so. If you go to another ASC, you may be accommodated unless the Application Support Center’s Immigration Services Officer (ISO) determines that you cannot be processed due to the unavailability of biometrics technicians, in which case the ISO will have you return for processing at a later time."
We took a chance this afternoon and drove to the Greer, SC USCIS ASC. When we pulled into the parking lot, it was pretty empty. We walked inside and were met by security. Their first question was "Do you have an appointment". I showed them the appointment letter from Atlanta and told them that we were hoping to do a walk-in. They said that they did not think that it would be a problem. They let my wife through and asked me to leave the building (no waiting area available). Fifteen minutes later my wife came out and her appointment letter was stamped with the biometrics processing stamp!