首先,这不是一个很好的例句.这句话是一个翻译公司先搞出来的,然后被好多中国教材抄了过去.这不是实际生活中用的话.虽然它的语法是对的(除了life要用复数),但是语义不很通.where在这句话里的意思是"在那种情况下",相当于in which (不是on which).
He had shown himself careless of personal safety in which the lives of his colleagues might be at risk.
他从来不把自己的安全当回事,这一点会危及同事们的生命.
我翻译的中文比原文要通顺.实在不知道如何把原文不通顺之处翻译出来.:-(
如果用其它连词如when：
He is first of all a sportsman,tireless,and careless of personal safety when riding and big game hunting,essentially a man of action.
那么就没有暗含的因果关系,而仅是简单的时间状语了.