There are over 100 strains of HPV, most are harmless, the ones that appear externally are harmless:
'There are about 14 high-risk HPV types including HPV 16, 18, 31, 33, 35, 39, 45, 51, 52, 56, 58, 59, 66, and 68. Two of these, HPV16 and HPV18, are responsible for most HPV-related cancers.' (NCI article).
You are right that cervical cancer is now recognised to be largely caused by certain strains of HPV, and this is now tested for on smear test, the action taken is that the smear is repeated months later and often the virus has been cleared by the body
'Most types of HPV cause "common" warts. These warts can grow anywhere on the body and are often found on the hands and feet. They are contagious and spread by touch, but they do not cause cancer.
About 40 types of HPV are called "genital HPV." Genital HPV spreads by skin contact, usually during vaginal, anal, and oral sex. HPV is the most common sexually transmitted infection. Genital HPV can infect any part of the genital area, including the vulva, inside the vagina, or the penis. It can also infect the anus and some areas of the head and neck.'
What types of cancer are caused by HPV?
Research links these types of cancer with HPV
Cervical cancer. HPV causes nearly all cervical cancers. About 70% of HPV-related cervical cancer is caused by HPV-16 or HPV-18. However, most genital HPV infections will not cause cancer Smoking can also raise the risk of cervical cancer in women with HPV.
Oral cancer. HPV can cause cancer of the mouth and tongue. It can also cause cancer of the oropharynx. This is the middle part of the throat, from the tonsils to the tip of the voice box. These HPV-related cancers are rising.
(All above from Cancer.net)