- please let me know if some mail order will be stocking this book
Yes, this works. "Will" lets us know that it is happening in the future.
- please let me know whether some mail order will be stocking this book
Yes, this works too, since there are exactly two possibilities, as you pointed out.
However, a mail order usually doesn't do the job of stocking books. This may be the company handling the mail orders, or some 3rd party. You could just use "they'll be stocking this book" or "they'll have this book in stock" (more natural than "stocking," which is still natural sounding but not frequently used) or the passive "the book will be stocked."