If your composition doll is important to you or a collector's item of some value, you may want to leave cleaning and restoration to a professional. Just be sure it's someone who actually has experience and not someone who bought a miracle product and calls himself a doll artist.
Before choosing a doll doctor, it's acceptable to ask about his or her background and for photos of prior work. And after describing the issue, ask what materials the doctor works with and how he or she would most likely approach the repair. Doll doctors don't have degrees, so don't be afraid to do your due diligence.