First, this is premised on how strong of a monarchy you believe Germany possessed. In other words, how little weight you give to the Chancellor, the Reichstag, Bundesrat and other power centers. Frankly I believe too much power is given to the Kaiser in most discussions and this is based on the notion that Germany was more absolute than it was, dismisses the federal and democratic and limited form of monarchy Germany in fact possessed and repeats too much the wartime propaganda that makes Wilhelm out to be both bully, tyrant, fool and warmonger. Albeit, Wilhelm was a touch erratic, insecure and impressionable. In counter I can find many examples that show Wilhelm was not nearly the villain he is made to be and could indeed steer a peaceful and liberalizing tact.
The obvious choice would simply be that his Father lives and then next would be that his brother takes up the throne, both being more widely regarded as either rationale, liberal or less feisty than Wilhelm is thought to be. Even an alternate Wilhelm, changed through taking the throne later, not being "crippled" at birth, not falling under Bismarck's attempts to alienate him from his Father, etc., etc.
And that brings us forward to 1914. We might well see a far less blundering and alienating diplomacy from 1888 through 1914. The motivations to align with Austria are manifest, if not inevitable. The bitter relationship with France is hard to ameliorate after 1871. Russia is the next Great Power disruptor, having more to gain breaking the status quo than preserving it, much as Germany did to be born and even Italy accomplished, so the path of Russia toward a war may be the same in general if not detail. And the British still face the economic threat posed by Germany combined with Germany's lack of true power to make them the choice (a choice they in fact refused) as counter to Russia and get Britain to fall into the quasi-alliance that promised to leave London a friend of a victorious Russia rather than foe.
The road to 1914 was convoluted but had some threads that can occur and in fact did occur without Wilhelm or even Germany having a hand. But if we go back to 1888 or even 1911, we can see the road ahead take on more options, enough that the Great War can easily be averted, altered or played out unlike our TL.
