Reddit reviews Pirate Hunting: The Fight Against Pirates, Privateers, and Sea Raiders from Antiquity to the Present

Empire of Blue Water seems to fit your request. It is largely based on historical accounts of Henry Morgan and attempts to be historically accurate. At the same time written in an engaging way by someone who is primarily a writer. Not being a historian I found it very interesting.

If you read slightly further back into this subreddit's history there are actual real historians who post here. They made a list of historically good books someone interested in the history of piracy could read. If you search on Amazon at other books the authors listed there have written you will most likely find many more interesting books on the subject. I am planning to get this book on pirate hunting next, written by one of the listed authors.