Any Wizard without their spellbook isn't automatically helpless
The core issue with this plan (going by rules as written) is that a wizard's spellbook is only used for learning and preparing new spells. A wizard that loses their spellbook will be unable to prepare new spells, but will still have the same spells prepared. There's even a specific clause (and price) for writing these down in a new spellbook should you lose the old one (see the Your Spellbook box on page 114 of the Player's Handbook, under Replacing the Book). And they'll always have their cantrips, no matter what happens to their book.
So even without sorcerer levels, a wizard bereft of their spellbook isn't rendered helpless, unless they prepared a very specific array of spells before losing the book. Adding sorcerer levels means they get additional spells which are known entirely independent of the book, and can cast all of these spells using the same slots (PHB 164). They even get more cantrips.
The only way for a wizard to be rendered helpless this way is if the exact spell they need is in their book, but not prepared that day, but I don't know what spell that would be.