I think if it was carcinogenic, we would all be dead. . . We work hard on trying not to track it and wash out hands, but the eggs come through the same vent as the poop.
If it were my feet and hands would be all curled up and dead. When we were kids on the farm I would sometimes wear flip flops and no gloves to clean out the coop. I've had poop squished through my toes and smeared on my hands.
I think your chickens are more likely to get cancer from the stuff that gets washed out of the air when it rains than you could catch anything from their poop.