You've got to soak it, I mean literally dice it in metho otherwise yes it will be sticky. Sit all the parts in a shallow tray, submerge where possible and the paint falls off with little to no help...get one of those kitchen pads with the green on one side. If you're not up to your elbows in metho, you're not doing it right You'll be back to virgin black plastic in no time.
With the A/C you need to pop the plastic screen out *carefully* when you're done glue it back in as you would have damaged some clips for sure. Same for the red and blue bit, cut of the melted plastic pins that hold it in, the glue them in when done. There's nothing easier than just painting the whole thing without worrying about masked edges.