How common is vulva skin cancer?

Not very. Vulvar cancer is uncommon, but very serious. Women with hpv are more likely to develop vulvar dysplasia and vulvar cancer. Smokers are far more likely to develop vulvar cancer. Plus they are harder to treat and more likely to have recurrences of the cancer.
See your OB/GYN. Hpv infection has been strongly linked to genital cancers. Vulvar cancers are rare and are usually diagnosed by biopsy of a nonhealing ulcerated area and may require wide excision of tissues that will require management by both your gyn oncologist and plastic surgeon.