Smoke detectors have a radioactive source, and we put them inside our homes, because the radiation level is so low that the increase of the risk is minimal.
Walls have a tiny amount of radioactive material, but they protect you from the radiation of the exterior. I don't know if the walls increase or decrease your cancer risk.
There are many thinks that may cause cancer. It's important to calculate the risk of each one, because you can't avoid all of them.
Only industrial smoke alarms use radioactive sources and even then only some types (you need different types for different situations).
The radioactivity in a smoke alarm is already negligible when you hold it in your hand, never mind when it's mounted on a ceiling.
Additionally the americium-241 used in smoke detectors is mainly alpha decay and a sheet of paper will stop it, the remaining radiation that is dangerous is gamma and it's exposure is so far below annual average background that you might not even bother. Flying in a plane will expose you to a thousand times more radiation.
If 55 other developed nations can ban use of asbestos, we can too. There's no need to calculate the risk if we can just avoid it entirely. Why poison yourself if you don't need to?
Walls have a tiny amount of radioactive material, but they protect you from the radiation of the exterior. I don't know if the walls increase or decrease your cancer risk.
There are many thinks that may cause cancer. It's important to calculate the risk of each one, because you can't avoid all of them.