Deteriorating door handle -- solved -- see update below

You've done most of the work already. Now just mask off a bit of the area around the handle with newspaper and give it a shot of the Krylon paint. It will only take you about 1/2 hour for the whole job and that handle will not only look and feel like new but will stay that way for a whole lot of years to come! :)
Beware though, after you get it done you will find many other spots on the trailer to do! :W
Barney