Apart from preventing skin diseases, how is the ozone layer significant to man?

All life is adversely affected by ionizing radiation which is the kind filtered by the ozone. Some have evolved melanin and other ways to prevent burning but they wouldn't be evolved for the higher levels. The scare that suggested the ozone layer would be adversely affected by humans was hyped out of proportion. It certainly has had no effect on warming. If it was destroyed, which is impossible since it is continuously formed by the sun, the amount of extra heat would be the least of your problems. You would likely get a m extinction event that would wipe out the vast majority of species.