There are actually thirteen circuit courts of appeals: #1-#11, as well as the D.C. and Federal Circuits.
This is all nonsense anyway - there are virtually no circumstances under which the Supreme Court is needed to give a snap decision on anything. Even if there were: if there were a President, and some kind of Congress, it could confirm his nominees; if there were a President but no Congress, he could simply declare that the Senate was obviously not in session and appoint recess nominees; if there were a Senate but no President, then Congress could simply pass a law stating that the Supreme Court comprised for the moment the senior judges of the First through Ninth Circuits, or the entire banc of the First Circuit, or whatever they wanted.
Emergency SCOTUS succession is a nonissue.
What if there were no clear President nor any Congress?