Update: I called the closest CVS pharmacy and they were able to look up my records. They seemed reluctant but she said she would give me a duplicate. I rook a Lyft from the airport, ~10 min ride to CVS. She had it ready for me. Lyft back to the airport, though security again, and 40 mins to spare before boarding. I will be sure to report back on which places ask to see the actual card and where I have success w/ the Swiss app.