I did exactly that actually. The only link to the study I could find in 5 minutes of searching is paywalled. I'm not going to pay $31.50 just to make a point on HN.
Based on the tables in this paper, alcohol-caused cancer is responsible for 0.8% of deaths. I don't see how the numbers in the paper could be used to calculate a value of 4% for any statistic related to alcohol+cancer.
The link is on the right next to the google scholar search results.