Ben, shutters/plastic are safe to paint excetp that you want to watch to be sure that the paint you choose id safe for plastics. The problem comes in because lacquer based paint has a high amount of lacquer thinner in the spray cans. The lacquer thinner can craze the plastic. There is no problem with enamel type paint.
You do want to spray as it's much easier and neater to get in all the confined areas with a spray. Brushing painting is possible but ends up being a mess usually because of the possibility for runs, drips, sags, etc.