Yay, drinking contest!
Kidding aside, it can´t be mentioned enough in these discussions that expansion of the German navy was not just a personal pet project of Wilhelm II. in the 1890s, but an idea with relatively widespread support and it seemed useful for a number of poltical interests within Germany. The question remained what kind of fleet to build. The debate initially leaned towards a cruiser-heavy fleet with even the emperor initially supporting that choice. The balance tilted around 1897 when Admiral Hollmann - a proponent of that strategy - was unable to get the requested funding and was replaced by Admiral Tirpitz. Tirpitz was the leading proponent of the battlewagon faction of course and in 1897 published his risk fleet theory, which became the leading theory. He also proved to be a much smoother political operator and managed to get the naval law of 1898 passed, not least by providing an apparent long term plan. Even then the risk fleet was not the general accepted theory as the law provided for a relatively balanced fleet.
The real change came during the Boer war, when the RN stopped and searched German vessels. Suddenly the extensive German merchant fleet seemed very vulnerable and the risk fleet gained a lot more support. Tirpitz used that to justify a massive expansion of the fleet - almost entirely for the battle line - with the 1900 naval law, which went through the Reichstag with a 2/3rd majority. Even that was largely seen as a defensive move by many in Germany and an alliance with Britain remained the favored outcome. Of course it was not perceived that way in Britain and the Royal Navy found it a useful tool for securing its own funding. We know how it turned out.
But I think we can see a number of possibilities for averting or limiting the Anglo-German naval race here. Three scenarios would be:
Had Hollmann successfully managed to get funding through the Reichstag by providing his own longterm plan akin to the 98 naval law - the Reichstag liked the long-term stability it suggested - Germany might have built more cruisers instead of battleships. An epansion of the German navy could still raise tensions with Britain, but probably not to the same degree. The German navy would still have built a number of battleships, but mostly more and better cruisers than otl. Probably the alliances would develop very different from otl and we might not even have seen a Great War at all. Keeping otl trends an at least vaguely pro-German British Empire would mean Italy is more firmly in the German camp as well and until the late 1910s France and Russia alone can´t really compete with a solid central power alliance. So I´d say danger of a direct clash is limited. With Russia getting stronger that might shift late in the 1910s, but than again Britain might also be drawn closer to an actual alliance with Germany then. Of course more German presence around the world offers plenty of chances for new conflicts, so there could be all kinds of wrenches thrown into that. A more aggressive Panthersprung? A new German attempt to gain a foothold in the Americas? A German cruiser accidentially sinking a British passenger liner? This has the potential to go better for Germany, but they still have plenty of chances to fuck this up.
Had Tirpitz not gained the handle of the mentioned incidents during the Boer war, an expansion beyond the 1898 law might have not happend or at least as reaction to France or Russia and not as radical as otl 1900 naval laws. Britain´s naval lobbyists still might use German naval expansion as a tool for getting funding, but the public focus would not concentrate as much on possible conflict with Germany. Germany would be one of several middling navies, given industrial developments probably develop in the medium term into the second navy in Europe, but not to the degree to threaten Britain. Britain would in that case probably try to maintain a certain balance of power in Europe, but not strongly alligned either way without another reason or until another navy starts to expand rapidly. If Russia still gets trounced against Japan it is a good candidate, as it otl planned a massive expansion in the late 1910s. The German armies probably would have been better equipped in this scenario, danger of getting embroiled in non-European conflicts is no higher for Germany than otl and Britain would be not as hostile. Still no guarantee that Germany is not seen as threat to the balance of power by Britain, but I´d say chances again favor a better outcome.
Had Britain and Germany openly discussed naval expansion with each other either before or in the first years after passing the 1900 naval laws, the naval race or at least its duration likewise may have been avoided. Bethmann-Hollweg tried to engage in discussions to that end in 1912, but of course by that time it was too late. Open discussions might lead to a better understanding of the respective goals and positions, in the best case with some coordination short of an outright alliance, but with chances to grow in the medium term. In the worst case there would have been some acrimony, but at least not as strong as otl and with the chance the British find a new naval rival before an atl war in Europe happens. Germany would probably still build a fairly sizeable fleet in this case, but limited by whatever understanding they reach with Britain.
