If the sun's surface was ~ 4000K (and earth closer to compensate), the UV component of the radiation would be less. However, UV makes ozone via photolysis of oxygen. Also, the stratosphere would probably start up higher (and contain less mass) because UV heating is what's responsible for the inversion. So what is the relationship between surface UV exposure (measured in DNA damage) and star temperature, which effect "wins"?
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2$\begingroup$ Interesting aside: smaller, cooler stars may have more UV than you think. This recent article on M dwarves points out that there are non-thermal emission processes, as well as frequent violent flares in some cases. Your question is still valid, but it is probably better thought of as finding a correlation between surface UV and stellar UV, or surface UV and spectral class of the star. $\endgroup$– user10851Commented Jan 2, 2013 at 9:08
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