The Second Republic was the not the sole creation of Louis Napoleon. He came into the country after the July Monarchy had already been overthrown and the Second Republic declared. In fact, his presidential campaign was waged from prison, and benefited a lot from the fear of the monarchists and moderate middle class of the "June Days Uprising", when Parisian socialists attempted to takeover Paris.
So, if you kill off Napoleon III, you will still have this very real fear among the monarchists and middle class of the kind of socialism-inspired violence that was seen in the June Days Uprising. This fear will then lead to the election of Louis-Eugene Cavaignac (the general who crushed the June Days Uprising, and the probable winner if Nappy III didn't get involved). I don't think that any of the other Bonapartes would be able to organize the kind of political support that Louis Napoleon. It must be remembered that Louis Napoleon was a very good politician, and that he was able to bring together an anti-socialist coalition.
With Cavaignac you're probably going to see the Republic continue. Without Napoleon III's drive for dictatorship, I don't know how the destruction of first the socialist clubs and then the republicans ones would proceed. Cavaignac was a moderate republican, and I think would try to run a democratic government. The problem is that the socialists want to overthrow the established social order, and their desire is going to drive the middle class back into the arms of authoritarianism.
So Cavaignac is president, but social disorder could continue. On the other hand, I don't think Cavaignac would move against manhood sufferage like Napoleon III did, so there is the possibility that the socialists, now much more involved in government, remain mostly peaceful. Cavaignac could maintain a coalition of anti-socialists- monarchists and the middle class. I don't know if this coalition will last, but, without Louis Napoleon I think that you may have a situation like the Third Republic, where no one really likes the Republic, but there is no alternative anyone can agree on.