Damage to the ozone layer has resulted in mutations in skin cells that lead to skin cancer. Will the mutations that caused the skin cancers be passed on to offspring?

The mutations would not be passed onto the offspring because the mutation was "contracted" during the organisms life, meaning its not genetically plausible to say that the offspring would get the mutation passed onto it. Its comparable to losing a finger. just because you lose a finger in an accident, does not mean your future offspring will also be born with a missing finger.