Besides Cervical cancer, I don't think there are any other cancers that can.. And even cervical cancer doesn't spread through a sexual contact. Cervical cancer is a secondary disease. HPV is a sexually transmitted virus which might or might not cause Cervical cancer, whether a person gets one or not depends on his/her immune system and state of health, so even a person who gets an HPV through sexual contact, doesn't necessary will get a Cervical cancer.
Also, if someone has a cancer, their immune system might be weakened because of the drugs and chemo they might taken. Therefore, these people are more likely to have infections or sicknesses that might pass on through genital fluids.