If you are going to bring numbers into it, then bring numbers into it. What are the cancer risks of alcohol? How does it correlate with the number of drinks per day or week? How does cancer risk correlate with aspartame? What is the ratio of risk from daily chewing of aspartame gum vs a glass of wine? If you don't know, then your argument means nothing.
And even then I'm only speaking of overall risk. They are additive, not zero sum. If you eat aspartame and drink alcohol your risk is higher than doing either one by itself, no matter what the numbers are.