I want to buy a book using a different account than the family share accounts

Nancy,

If you already have a different account to use -- one that is not part of a Family Sharing group -- then you can go ahead and do that.

In general, having multiple Apple IDs can create confusion in the future and is usually not a good idea. Perhaps you can buy the book in your current account and hide it from sharing.

Hide and unhide music, movies, TV shows, audiobooks, and books - Apple Support