Yes, no, maybe. Very few people know anything about cancer, and there are many types of alcohol. Mouthwash might contain very large amounts of alcohol, compared to alcoholic bevarages, and there are a lot of nasty effects from using it. You can search the subject at your favorite search engine and get a flood of advice but very little agreement on your basic question.
In 2012, the quantitative analysis of eighteen studies was done to see if mouthwash containing alcohol can lead to oral cancer. There was no statistically significant associations found between regular use of mouthwash and risk of oral cancer. There was also no association between reported use of mouthwash specifically containing alcohol and risk of oral cancer. So to answer your question, you can use any mouthwash without any risk done to your oral health.