Of course, the other German states might have thoughts of their own.
OTL, the Federal Diet went 8-5 for mobilisation against Prussia. Would they be so ready to burn their bridges with Bismarck dead and future events up in the air? It would only need two more to opt for "wait and see". Indeed, if such a result seemed likely would Austria submit the motion at all?
Had the assassination attempt succeeded, all European history would have been open for great changes.
You don't have to like him, but Bismarck really was a singular character and very much able to think outside the box. The way he coopted the Liberals with nationalistic successes and rhetoric, the far-reaching attempts to break socialism by creating a paternalistic welfare state "nach Gutherrenart", the way he mostly could grasp which changes the other powers could accept and which not - you cannot easily replace this.
Depending on the composition of the new leadership clique, we might see
~ a Prussia that avoids war and continues to work slowly with Austria within the framework of a reformed Bund,
~ a Prussia that goes to war, wins militarily but fumbles the peace by turning all of Germany into bitter enemies,
~ a Prussia that goes to war, wins militarily but finds itself indebted to France
~ a Prussia that goes to war and is militarily crushed in Bohemia, loses territory and becoming a protegé of Russia