I'm very curious on how the transition took place and I prefer a single book rather than scouring the Internet for tiny bits of info here and there.
Makers of Modern Strategy is a collection of essays which explore the development of tactics and strategy from the 15th century all the way to the Cold War. Its definately explores the topic youre interested in, and then sme.
If you were looking for a tighter exploration of the transition from Napoleon to Schlieffen, The American Way of War explores the foundation and development of the American Army from its foundations to the 1970s. Weigley really focuses on how the American Army adopted Napoleonic strategy in the 1820s-60s, how that influenced the Civil War, and how the debate between post-Napoleonic and Civil War thought. Thatd be the book I recommend to you.
Most books on the first years of World War One also explore the influence of Napoleonic and post-Napoleonic thought on the armies of 1914. A good examination of that is in the first chapters of The Marne, 1914.
Honestly some of the best case scenarios involve finding bits of information from 'here and there'. Michael Howard's The Franco-Prussian War: The German Invasion of France 1870-1871 is a great source for that period. If you want the transition of late 19th century to WWI thought Robert Doughty's work Pyrrhic Victory: French Strategy and Operations in the Great War has an enormous first chapter on the matter. If you're more willing to drop a pretty penny From Waterloo to Balaclava: Tactics, Technology, and the British Army 1815-1854 by Hew Strachan is probably the greatest work on post-Napoleonic British thought leading up to and including Crimea in existence.
Fact remains though that works like Hew Strachan's, which focus entirely on the military aspect, are both expensive (<$100 minimum) and rare because if we're talking Europe between 1815-1914 the focus is on the social aspect not the military in this period; it's kind of like trying to find work that isn't focused on the Dutch or Prussians in the late 1600's. It's just the focus of that period in European history is on those topics so finding other stuff is difficult and whatever you do find that is also cheap is also likely to be, frankly, shitty. So your best bet is getting intro to WWI books and gleaning info off of that and getting whatever reputable info you can on specifics wars and piecing it together yourself. That or buy $100-$300 textbooks; I choose to do this option but it takes a lot of time :P
I had a professor last semester named Geoffrey Wawro who wrote a book called "Warfare and Society in Europe 1792-1914" that I really enjoyed and is pretty much exactly what you are looking for. Another book I've read most of and have found very useful is called ""The Patterns of War Since the Eighteenth Century" by LArry Addington.