I highly advise at least a ratchet strap on your spare. The factory winches have aged to the point now they are not trustworthy. I found out the hard way one day a few years back. The spare WILL bounce when it falls from under the truck and makes for a fun time when it comes back up and turns sideways under a moving truck.
I have a full size 31" spare on a turbine wheel under mine. I had to remove the "splash guard?" that sits right behind the bumper for it to fit. But wouldn't do it without something other than just the factory winch.