Preying on her innocence, he told her he was performing a procedure but sexually assaulted her, the CPS said.
Having worried about what happened for years, she reported the offences in May 2020 and Davis was arrested.
The following month a second woman read about the arrest of Davis and came forward to report a similar incident in 1995 when he performed an unnecessary gynaecological examination on her, the CPS said.
During the police investigation Davis denied committing the offences, claiming any procedures he carried out would have been necessary.
He was found not guilty of a separate count of assault by penetration, sexual assault and causing a person to engage in penetrative sexual activity without consent.
Two counts, one of assault by penetration and attempting to cause a person to engage in sexual activity without consent, were not proceeded with, the CPS said.