safer to go fast or go long?

what do you mean by safer?

a) less likely to injure yourself- proably depends on your level of fitness
b) less likely to get hit by a car- statistically speaking more time on the bike increases your chances, but also more time on the bike makes you a more experienced rider and more aware of your surroundings, so that should decrease your risk some
c) less likely to get skin cancer- wear sunblock for either one
d) less likely to get a saddle sore- short ride
d) less likely to crash during a race and become one with someone elses bike- HIM or IM

NOT AT ALL. IF and only IF you train smart, with a goal, build up gradually and consistently it doesn't matter what’s your race distance goal, you chances for injury will be lesser. Training for an Oly or a HIM isn’t that much different, you'll just add more volume and train at different intensities for the Oly, that’s all.  ALL 4 distances are aerobic events so the main focus remains the same...

Agree with Jorge above.  And, actually, if you intend to be fast at the sprint/oly distances your volume will not be much different for the bulk of your training than someone doing HIM/IM.

As it has been said training for all the diffrent distance triathlon events are more or less the same. You need both base and speed training.
Sustaining an injury has nothing to do with it.