Chemicals capable of producing mutations are both naturally-occurring and synthetic, and are found in the environment, food, and water supply, or have been used as drugs
Radiation (often referred to as "ionizing radiation"). If the mutated cells do not die, they may become transformed and eventually cause cancer (as in the skyrocketing incidence of leukemia after the atomic bomb was dropped on Japan).
Viruses can inflict damage by inserting themselves into the DNA of an appropriate host cell, also known as its "genome", to cause cancer.
There are, I'm sure, many things that COULD cause cancers of various types.
I can't prove a negative. IOW, I can't prove that SHS DOESN'T cause cancer. It is on the anti-smokers heads to prove that it DOES.