Assuming that the savings from having a much smaller German navy paid for a much enlarged German army, then a POD might have to be injected around 1898 to side step the OTL naval expansion bills. Regardless, wouldn't this remove the main cause for GB getting too cozy and associating itself with the Entente powers? If so, then Germany might not only initially gain immeasurable advantages in a European ground campaign, but also possibly benefit from a cautious, yet neutral Britain, and not suffer a naval blockade, which in turn might drive less emphasis on uboat construction. Although the German navy was advocated as a way to build nationalism among the relatively recently unified German states, which still maintained separate ground forces, it may have been more wishful thinking and less effective than thought. However, assuming the above is correct, is there cause for concern for the loyalties of the German states had Germany not increased it's navy so heavily? In a world of ultra-nationalism I would think not, but I'm not well read up on the naval arms race and the dynamics at stake to the naval advocates.
As far as I have gathered in researching my TL, the navy was mainly built because the Emperor was fond of navies and wanted his own and Tirpitz, who was an ardent supporter of a battleship navy convinced the Kaiser so got the office of Chief of the Imperial Naval Office. There were different opinions on how a German navy had to look like and Tirpitz was just good in getting the ear of the Emperor. Furthermore Tirpitz initiated a well-oiled and financed propaganda machine which included the foundation of the Navy League. They draw quietly heavily on nationalist feelings. Then there was the notion that Germany should have colonies and since the British Empire had colonies and a big navy Germany would need for its colonies a big navy, too. I doubt the German Empire would splinter again. There was a fear of that, especially in Prussia, therefore Prussia had ambassadors in most of the German states, and there were some real differences in confession or political leaning. Nonetheless there was no real danger at this time of the states leaving the Reich.
You can use all kind of PoDs to do away with the navy: You can have another naval officer succeed in gaining the ear of the Emperor. Gallster for example had a quiet different and interesting view on that subject. Or you can have the Emperor not interested in navies. Or you can have another Emperor. The Emperor is actually a key person in this because he protected Tirpitz (and later on the naval attaché to London Widenmann) for a rather long time.
You can also try with a later PoD, changing one of the chancellors or part of their personalities to get rid of Tirpitz. An alliance with the military might be useful for that.
In removing the naval arms race completely you will have better terms with GB. But the naval arms race was not the only reason for them to cozy up to the Entente. Russia was a threat to the Empire in East-Asia, in India and in Persia. France was a threat in Africa, the Near East and the Mediterranean. That was at least on of the major reasons for Grey to initiate agreements with them. One should remember that those agreements even in OTL never were a formal alliance of any kind. Grey just come to an understanding with France (and at least for some time with Russia) over their respective colonial spheres. That was the "entente cordial". This understanding deepened with each international crisis in which the Germans behaved a little bit erratic on the diplomatic side causing a war scare, namely Morocco 1, Bosnian annexation and Morocco 2. Especially Morocco 2 was responsible for (secret) military talks and informal cooperation agreements. Together with the German naval law of 1912 it led to the agreement that the French fleet should protect the Mediterranean and the British navy the Channel coast. Depending on what or when your PoD is you can butterfly away those problems, too. Besides that there is a school of historians who believe that GB's strategy was to hold up the balance of power which might have been another reason for their support of the entente in the Balkan and Morocco crisis'. Which will again strain GB-German relations. Personally I think that - although some of Grey's thoughts were still bent on this scheme - he was more focused on preservation of the Empire, which of course may include a strategy of holding future rivals at bay. But in my opinion balance of power just for the sake of it was not his strategy.
On a siedenote: It is to say that it was not always Germany alone which was resonsible for those crisis and it had in some respects also good reasons for its stance. It was more often just poor diplomatic behavior which let the German side look more aggressive than she was.
If your aim is a really good relationship with GB than just find a PoD in the 1890ies, which will lead to the alliance GB-Germany, Lord Salisbury sought. For a very late PoD you can have a look into my TL here:
https://www.alternatehistory.com/discussion/showthread.php?t=189376, which focuses on a slightly different Bethmann Hollweg who is more self-confident and assertive and has a more forceful personality, although these changes there maybe not enough to have really good relations with GB or to stop GB leaning to the Dual Alliance (France-Russia).
Kind regards,
G.