Tedious! My wife used to drive me crazy painting shutters!
Go ahead and paint them, and exercise them as they dry.
You have to start at the top and paint a few slats on one side, and then get them on the other side to control drips and runs. I would do the frames last. Use an angle cut (sash) brush.
If they are now painted with enamel, wipe down with liquid deglosser just before painting with oil enamel.
If you want to paint them with latex, you will have to prime them first with oil primer. That would be two coats and the latex dries thicker. That would make it more likely for them to stick.