Here is the summary. (MM=malignant melanoma and NMSC=non-malignant skin cancer) Not a hugely strong relationship. Also, red wine was not shown to have an impact. So, I would say that this is just one more factor in a wide array of factors that could have an impact on skin cancer.
Source: Cancer Causes Control. 2014 Jan;25(1):1-10. doi: 10.1007/s10552-013-0280-3. Epub 2013 Oct 31.
Alcohol consumption and risk of melanoma and non-melanoma skin cancer in the Women’s Health Initiative.
Kubo JT, Henderson MT, Desai M, Wactawski-Wende J, Stefanick ML, Tang JY.
Over 10.2 mean years of follow-up, 532 MM cases and 9,593 NMSC cases occurred. A significant relationship between amount of alcohol consumed and both MM and NMSC was observed, with those who consume 7+ drinks per week having a higher hazard of MM (HR 1.64 (1.09, 2.49), p global = 0.0013) and higher risk of NMSC (OR 1.23 (1.11, 1.36), p global < 0.0001) compared to non-drinkers. Lifetime alcohol consumption was also positively associated with hazard of MM (p = 0.0011) and risk of NMSC (p < 0.0001). Further, compared to non-drinkers, a preference for either white wine or liquor was associated with an increased hazard of MM (HR 1.52 (1.02, 2.27) for white wine; HR 1.65 (1.07, 2.55) for liquor) and risk of NMSC (OR 1.16 (1.05, 1.28) for white wine; OR 1.26 (1.13, 1.41) for liquor).
Higher current alcohol consumption, higher lifetime alcohol consumption, and a preference for white wine or liquor were associated with increased hazard of MM and risk of NMSC.