Sidestep the problem entirely by not using screws.

Use a black plastic roofing cement or a latex caulk as a glue to glue the new plywood in. Have a helper apply caulk to the trailer frame while you apply caulk to the plywood and then drop the plywood into the trailer frame. Clamp the plywood down to the trailer frame for a few days while the caulk sets up.

When the time comes to replace that trailer bed, just cut most of the plywood out with a circular saw or jig saw and then use a pry bar to separate the remaining plywood from the steel. Then use a paint scraper to remove most of the old caulk from the steel. (Follow up by cleaning the remaining acrylic caulk off with MEK or toluene or lacquer thinner or acetone if desired. Remove the old plastic roofing cement with mineral spirits.) Otherwise, you can just caulk in another new plywood trailer bed exactly the same way over the existing caulk.