Ideally, you should be able to get an authenticator's public key and be able to enroll one without presenting the authenticator itself, allowing you to keep it in a safe/etc.
This would enable an easy workflow - enroll main authenticator as normal, then enroll your safely-stored backup by pasting its public key. If you lose your main, go to your safe, get your backup and "promote" it to primary and enroll a new backup one which goes in the safe.