I thought that once the House vote was taken, Ryan would become president and automatically lose his seat. If he didn't want the presidency, then he could resign, but he would still no longer be a member of the House. IIRC, the constitution doesn't spell out a process where they can decline. They just become the holder of that office.
I read the 1947 Presidential Succession Act as saying the Speaker would become president upon resignation of his office, implying that he could decline to resign and pass succession on to the next person. It does look to me, though, like once it gets down to the cabinet level, succession is automatic.
