This has a lot more intriguing butterflies than I'd have imagined, a German Phillipines, no Pearl Harbor/no carrier-focused U.S. Navy...
Possible POD's:
William Randolph Hearst or Joseph Pulitzer die almost immediately with the war's beginning and the media pressure for war drops precipitously since this is more about two U.S. newspaper chains' circulation wars than foreign policy, making it much easier for the reluctant McKinley to accept Spanish apologies/damages on the Maine and call back the troops.
An investigation commission on the U.S.S. Maine's demise is able to prove it's a smoldering coal bunker fire that exploded finally in the harbor rather than the claimed Spanish mine. The Discovery Channel did a convincing piece on that and coal bunker fire problems were increasingly common on long voyages, one of the big reasons for switching to oil for fuel not long after this. So the war doesn't start at all or is ended with the commission's report (unless it operates like modern commissions and reports so many years after the event it has no impact at all.)
Hurricane devastates the overloaded and very marginal ships pressed into service for transporting the American invasion force to Cuba, causing enough losses of men and equipment that they return to Tampa's logistical mess and in the ensuing months before enough ships, trained troops, equipment, etc. can be mustered, peace is negotiated. This would be a major amphibious invasion by any measure and the American Army was spectacularly ill-prepared for this, that they made it ashore and won is more unlikely outcome.
The Spanish did have Maxim machine guns, just not many of them, so several dozen more would have made a difference at any of the battles and may well have been on Cuba but dispersed to too many places. I think they might have had some modern Krupp artillery pieces too but that's as likely faulty memory on my part. Along with their regular Army there, there were roughly 2,000 in their Cuban Colonial Police force who after years of the guerrilla insurgency would be competent junglefighters themselves and could have been a battle-tipping surprise if used instead of kept to the insurgents and concentration camp duty.
Don't see how the naval outcomes change without relying on big storms far at sea to do the work (although that worked on Kublai Khan's Mongol invasion fleet headed to Japan and Phillip's Spanish Armada headed to England so it's not absurd.)
Spain agrees to give Germany some of the Pacific islands (Guam, Marshalls) for coaling stations/naval bases if it agrees to ally with it to face down American aggression, mostly to make a strong enough team to force immediate peace negotiations rather than a shooting war. It would certainly motivate McKinley that this saber-rattling was getting out of control and spiraling into a big war (like McKinley'd fought in in the American Civil War.) That would allow Spain to avoid the war, preserve it's fleet and most of it's colonies while building a stronger alliance with another major European power much like Franco and Hitler 38 years later.