I ALWAYS do this with FedEx and I'm surprised more people don't. The FedEx Shipping Center near me is at the airport. The package goes about 150 feet from the plane to the desk where it's always available for pickup at 9am when they open - that's the end of the process.if that is the case, then I'd always do "hold for pickup" and get the package yourself much earlier and with less stress on the livestock.
I have switched having any livestock delivered. I now have every livestock shipped to the hub and marked "hold for pickup". doesn't matter if it's UPS or FED-EX, I do the hold for pickup every time now. I have not had a single issue with either one since going exclusively to hold for pickup method.
Otherwise, I have to wait for it to be loaded on a truck, driven to a local distribution center, sorted, loaded (hopefully) onto a local delivery truck, and then (again, hopefully) delivered to my address sometime in the afternoon if everything goes right. Picking up at the shipping center greatly decreases the odds of delay due to incident along the chain. And if there's a delay in Memphis (or whichever air hub it's coming through), there's still a good chance it'll arrive at my shipping center later in the day since it's still just being moved from the plane to the desk at the same facility. But if I did home delivery, I'd have to wait at least another day because once you miss the delivery truck dispatch in the AM, you're stuck till the next day.
TL/DR, FedEx isn't great for many of us, but there are ways to greatly improve your odds of having a successful transaction.