I doubt his death would make much difference vis-a-vis Britain, save that perhaps Britain would end its isolation later. Other than that, too much bad blood existed on both sides for there to be no Anglo-German rivalry. The dominant Anglo-American narrative tends to blame the Germans for the rivarly and its consequences, but in truth, Britain was as much to blame as Germany. If Germany acted like an uncouth gangster, Britian no less acted as a jealous hen-pecking wife twenty years too old to be acting thusly. If the Kruger telegram was impolitic, it was all bluster, of no real substance; in contrast, Britain played Germany false quite many times, stringing it along for phantom prizes that Britain had zero intention of paying. Even the so-called alliance project of 1901 was but a mirage, something Salisbury and the rest (except Chamberlain) never took seriously.
In addition, the first Naval Bill was quite modest, even to the British. Other than few rabidly Germanophobic newspapers that habitually made mountains out of molehills, most British statesmen and the public did not feel alarmed over it. It was only with the second Naval Bill that the British took alarm, but that must been seen in context, namely that the whole continent hated Britain over its arrogant behaviors over the course of the 90's (basically telling the Continent F**k U! We have the biggest navy, so there, there's nothing you can do. Shove it up yer Arse!) and in particular, whole of Germany felt like Britain just bitch slapped and trampled all over Germany's honor. From Britain's double dealing over the Portugese colonies, to Britain's naked resort of force as the ultimate diplomatic stick in Fashoda vis-a-vis France, to culminate in the Samoan affairs where Britain humiliated Germany and showed to the Germans the impotence of Germany in the face of the British navy, the Navy League and the Right would've never have succeeded in passing such an ambitious military program through the Reichstag, but for the climate of helplessness in the face of the British naval domination. We need not argue whether it was the right course or not -- it wasn't -- but we must see that the German navy was a foregone conclusion given the political, cultural, social climate of the day. This was especially true in the aftermath of Mahan. He had huge influence not only in the US and Britain, but also in Germany, and converted great many skeptics to the idea of weltpolitik, not in its incarnation as the kaiser's vanity project, but as a strategic necessity if Germany were to retain its Great Power status.
After Mahan, it entered into popular consciousness throughout the West that the sea-power was requisite to a nation's greatness. All Powers spent heavily on navy; in fact, for most of this period, it was the French who spent the most on navy on the continent, not Germany.
Where the Kaiser's death might have made the difference is in the East. While the Reinsurance Treaty itself wasn't all that important, it was an important symbol to Russia that Germany was willing to cut the long-cherished wire to the St. Petersburg and lay a new one to London. That this was not what the Kaiser intended we now know, but at the time, this was how the Russians interpreted the first year of the Kaiser's reign. Given what we know of Bismarck's health, his continued stay in the office would've continued the wire to Russia at least until 1897, and thus there might not have been any Franco-Russian Alliance, or if it came, then at a later date. We have to understand Russia of the period. Yes, there was economic friction with Germany; yes, great deal of both countrys' public hated each other; yes, some members of the Establishment in both countries were rabidly anti- each other. But: by and large, Russia was satisfied being led by the German leash, despite protestations to the contrary. Russia did not want a free hand in Europe; it dreaded it; it was suffering through some of the worst economic crises in its history and desired nothing more than to be left alone in Europe so that it could rape easier targets in Asia. And it would have been exceedingly easy for Bismarck to accomodate the Russian wish, especially since Bismarck had a knack of bribing one country with another country's property.
Heck, Russia could've had constantinope at any time in the 80's, had it really wished so. But it did not want Constantinope, despite what the other countries thought; all it wanted was the Straits closed. Barring that, a status quo and the Porte powerful enough to deter any British navy trying to force its way through. Thus, Bismarck time after time tried to give away the Straits to Russia for a grand Balkan settlement, with Salonika as the dividing line. Alas, Russia did not want any more territories, not after the Bulgarian fiasco. Russia, to its credit, realized that pan-slavic feelings were just that --feelings: Balkan countries did not free themselves from the Porte just so that they could have a Russian overlord in its stead.
If Bismarck had lived longer, into early 1900's, then he might have done that which he had always contemplated, but always dreaded to do so: ditch Austria once and for all. Only he had the necessary historic prestige and accumulated greatness to force through such radical act, given how popular the Alliance came to be with the public (though not with the Establishment).
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