For the record, there was never a "time Oswald was supposed to be transferred".
Curry simply told the world's press that as long as they were present the next morning by 10 AM, they wouldn't miss anything. That is not to say the transfer was scheduled for a particular time, but instead it was "scheduled" for ANY time after 10 AM.
Anyone planning to kill Oswald would take that to mean he needed to be in the garage by 10 AM if he wanted to kill Oswald. Otherwise, he could miss his chance, Oswald would have been transferred to the county jail, stood trial, been convicted, sentenced to death, been spared by SCOTUS in 1972 and he might still be doing time in the Texas state penitentiary.