"Expired" and "no longer in use" are not the same. No professional medical provider will knowingly administer a medication that has passed the expiration date on the vial.
It sounds more like you are talking about an "older" vaccine, i.e. the ones formulated for use prior to the current one. These may not be as effective as the ones formulated to fight newer variants, but if they are available and in use, they would fulfill the requirement.
I recommend confirming which situation it is before deciding. AFAIK, there is no alternative except for seeking a vaccine waiver, and those are nearly impossible to get if you've had any type of vaccine previously.