Because Barry destroyed Cicada's dagger in 2019, this should mean that it's never used to dampen Eobard's powers while he's in prison. This means, when he ends up getting put in Iron Heights on death row in the new time-line, in which the dagger had been destroyed in 2019, the prison staff should just take different measures to dampen his powers while he sits on death row, allowing him to be executed without any problems.