Don't both FedEx and Southwest (and every other carrier for that matter) list a 1st class medical as a requirement? I'd keep it current just to be on the safe side and to be able to apply to any other jobs that pop up. FedEx is alot of people's first choice but why limit yourself? Plus, you'll need an FAA medical at some point. You don't want to be surprised by issues that pop up at the interview or post-hire!