Just exactly how will there be opportunity for fighting?
The germans likely have a formidable Army at this time, but if the United States doesn't invade Germany near Hamburg (very funny that idea) I fail to see how either side can come to grips!
The USN really doesn't exist in 1889, but then, neither does the kreigsmarine! I seriously fail to see how the Germans are going to project force across the Atlantic, and that if they did, how they could sustain a force large enough to sieze and hold very much ground in North America!
As for fighting in Samoa, that is on the far side of the world for both parties. At that time, I doubt either could maintain so much as a regiment there! Big deal!
I DO feel that a "war with Germany" in 1889 WOULD tend to stir things up in the US Congress, Just about the time this war happens, the US Congress is going to notice how little prepared the United States is for any sort of war more complicated than fighting the plains Indians, so---I'd imagine that both the Army and especially the Navy would get surprising amounts of new funding.
There would be a rather sudden expansion of the standing US Army, to the point that the effects of a raiding party of invading Germans could be dealt with, and that efforts to creat an ocean going navy of 1st class battleships would go into high gear.
While I'm not 100% sure how extensive Germany's fleet was during this period, I am reasonably sure that it too was pretty small, so it becomes a building race! In the event of an all out naval building race, wouldn't the Germans come under the immediate notice of other neighbors, closer to home than say New York City, whom could be counted on to object? I suppose that a serious effort on the part of the USA to also build a Navy might be viewed through some jaundiced British eyes as well, but would a USA with a large Navy be viewed with the same amount of consternation as would a GERMANY with a large navy? Probably not!
So, to recap things, we find that the Germans are unable to project military force across the Atlantic and the USA is likewise unable to do the same! Both sides are building new warships at a frantic pace, and there is a very small "battle" in Samoa!