I don't use CSC; but I have heard that it tends to be safe to use on kit glass (don't use it on diecast or resin); I'd try to carefully sand/polish the paint off unless it's really thick. The same method to wetsand/polish paint works to repair kit glass, if you're careful.
If it's acrylic paint you can remove it with Windex or rubbing alcohol.
As for chrome; whatever will strip that paint will strip the chrome. Unless the paint is acrylic where you might get away w/using rubbing alcohol or Windex. No guarantees though, but worth a try.