We don't ship anything. But I consult for a client that ships with UPS and another regional shipper as well as several other distribution companies. They have separate designated storage areas for each shipper.
You should also setup two different label printers. The FedEx one closer to the FedEx pile and the USPS on the other side closer to the USPS pile. You will still eventually have an issue. Hopefully, your driver will bring back the package and if not that your costs savings will allow you to cover it.
What we did in our warehouse since we use usps and fedex is that we contacted usps and they give us postal bins to put mail items in and the fedex items are placed in a box we taped out on the floor so that anything within the red tape fedex can pickup and just educate the drivers.
Fedex does have a pick up weekly fee which really annoys me, but depending on your volume you could drop it off and save the fee.