Truth is, though, that the German novelles of 1898 and 1900 didn't raise alarm bells in London. It was only with the Third Novelle that the freakout began. For this reason, I think that a German Navy obviously built for securing control of the Baltic and defense of overseas colonies against middle-ranking naval powers isn't going to bring Germany into conflict with Britain - at least, not by itself.
On further reflection - and reference back to Robert K. Massie's
Dreadnought - I think my paragraph here stands in need of some revision. In fact, the second German novelle ("Fleet Law") in 1900 *did* start to trigger concerns in Whitehall, and pretty arguably pushed an initial (pre-dreadnought) phase of the Anglo-German naval arms race. The 1900 Law (passed in the Reichstag on the heels of RN detention of German merchies in the Boer War) increased the authorized strength of the KM to 32 battleships, which was was a literal doubling of capital ship strength of the KM, and when completed would give Germany more capital ships than any power but Britain.
Lord Selborne, Lord Salisbury's First Lord of the Admiralty, felt compelled to address papers to the cabinet, first in November 1901:
The naval policy of Germany is definite and persistent. The Emperor seems determined that the power of Germany shall be used all over the world to push German commerce, possessions, and interests. Of necessity, it follows that German naval strength must be raised so as to compare more advantageously than at present with ours. The result of this policy will be to place Germany in a commanding position if ever we find ourselves at war with France and Russia...Naval officers who have seen much of the German Navy lately are all agreed that it is as good as can be.
In an October, 1902 cabinet paper, Selborne was at it again:
The more the composition of the new German fleet is examined, the clearer it becomes that it is designed for a possible conflict with the British fleet. It cannot be designed for the purpose of playing a leading part in a future war between Germany and France and Russia. The issue of such a war can only be decided by armies on land, and the great naval expenditure on which Germany has embarked involves a deliberate diminution of the military strength which Germany might otherwise have attained in relation to France and Russia.
Salisbury's and Balfour's (admittedly already high) naval estimates began to increase accordingly. It arguably helped give impulse to pursuit of the Anglo-Japanese Alliance Treaty in 1902, too.
Still, I think this only revises my argument in its timeline, not its essence. The 1898 Law, which authorized a strength of 16 battleships, was not enough to alarm the British. Its doubling, two years later, did.
I wonder what this might suggest about a KM fleet structure that would fulfill the OP's requirement. It gets complicated because both France and Russia were structuring *their* building programs in partial response to Germany's by the dreadnought era; but also because due to awkward geography both were forced to split their fleet into different theaters, Russia emphatically so. A KM which is *not* building at a Tirpitzian madlad pace might see France's 1906 naval law demand only, say, 12 battleships instead of the 16 of our timeline (and that probably more in response to Italy than Germany); though how it would deploy them in the absence of any deployment agreement with Britain could be harder to size up. The Russians are probably still likely to build something like the four Ganguts for the rebuilt Baltic Fleet, though...
So, perhaps 8 dreadnoughts, and perhaps an equal number of pre-dreads for the KM In 1914? This would be plenty enough to confine the Russians to the Gulf of Finland, and assured trade access to Scandinavia; mining of Heligoland Bight, and a quick shift of a squadron via the Kiel Canal (which would still need to be widened, I think) would be adequate to deal with any French approach in the North Sea in the unlikely event the British allowed it. But this would be a modest enough number, and clearly limited enough in purpose, to leave Whitehall under any conceivable cabinet feeling relatively unthreatened.