Yes, you can use bonded panels in place of the screw panels. Use 3M VHB, they have one for applying the panel to the beam and one for panel to panel. The VHB tape will cover the entire beam and existing screw holes. .030 is the typical panel for most trailers. Higher end trailers use either .040 or .050". The thicker it is, the smoother, less prone to dents, and less wavy it will look. VHB gives you one shot to stick it, so make sure it's straight and level!
You have to remove the trim to replace panels, so I'd replace it as well if it's dinged or scratched up. The trim isn't expensive, and the trailer will look brand new. Also with the panels off, you can insulate, fix or add any wiring, etc...
You'll probably have $1500-$2000 in re-skinning a 20' trailer, depending on gauge, but you'll have a LOT of labor!