It'd be hard to control for everything relevant. Diet would be indirectly affected by sunlight (sunny areas would naturally have different crops). Amount of exercise, too. Genetics play a large role in some cancers, but behaviors and choices are strongly linked to many common cancers like lung or colorectal. Breast cancer has been linked to a woman's history of pregnancy (higher risk for those who were pregnant when very young or never had been pregnant past middle age).

mini-rant

Even if we could design an experiment to know how much sunlight affects cancer mortality, it might not be worth the time and money. We already know ways to reduce cancer incidence in a population: less tobacco, less alcohol, less obesity, more exercise, sunscreen if you have light skin. We could further reduce cancer mortality by getting people to follow screening guidelines.

We've reached a point where public policy and outreach are the most valuable efforts to preventing cancer incidence and mortality. Quitting bad habits is hard. Going to the doctor for screening can be scary, expensive, or logistically difficult.

/mini-rant

Would especially sunny areas not produce people with more cancer (or certain types)?

Maybe. Some studies have shown people in sunnier areas have less risk of certain types of cancer.