I'm actually not sure that a successful Jing Ke would have made much of a difference in the long run. Recall that he attempted to assassinate the king of Qin in about 225 BC. By this time Qin had already successfully conquered Zhao and Han. Wei and Qi were tiny and Yan and Chu were shadows of their former selves. By the time of Jing Ke, Qin had already achieved superiority over the other states, and their long-term unification of China was essentially assured. So even if Jing Ke succeeded, it probably wouldn't make too much difference.
However, one thing that could mess things up is if there was a succession crisis in the aftermath (assuming that Jing Ke assassinated the King of Qin). If Qin delays in installing a new monarch, maybe internal dissent starts to develop, and maybe it devolves into civil war, and then who knows?