Is there an alternative approach to incorporate research methods into a book chapter without dedicating a separate section for methods? If so, how can this be achieved, and where within the chapter is it advisable to include the methods?
If it is proceeding in format of book in chapter, yes you should include methodology part. If is also a review of books, you should specify your methodology.
Why are you hesitating to include the methodology? It's always preferred to be as transparent as possible for readers. If you are limited by the book-length you could add a methodology description in the introduction but I wouldn't recommend that.
Often a book (or a chapter if you are only writing a chapter) provides background for why you chose your topic. This is a logical place to include why you chose your methodology.