If I need to let him have an arcane focus, I can. That's what I'm trying to figure out.
I'm ok with him being extremely limited, as they all will be. I just don't want him to be totally useless in the first encounter or two.
This is the sort of thing I see a lot, and my question is always the same - why is a wizard without spells useless? If all your wizard (or the player) can come up with for their character to do is cast spells, then there is a significant portion of any day where they have limited or no ability to do anything.
Sure, that's their "special ability" but that doesn't mean that they can't contribute or help in other ways.
As for recovering their spellbook - in my campaign it would depend on where it is. That might be more difficult, and might be easier to start looking for scrolls or other spellbooks. Of course, my campaign still has full spellbooks and traveling spellbooks, and the majority of my players' characters actually have a home to return to. So the wizard can go back and create a new traveling spellbook or two. Of course, a wise wizard might have squirreled one away someplace more convenient if far from home, or have some other contingencies for situations like that.
So it's really going to depend in part on your players and their play-style and expectations. Yes, the wizards in my campaign expect that they will have access to their spellbooks 99% of the time. And that's true. But there are exceptional situations, and they might lose a spellbook (or have it damaged or destroyed), characters are separated from their magic items, etc.
Since my players are more focused on their characters as a whole, specific special abilities (even one this important to the class), are secondary to the character finding a way to overcome whatever obstacles are in their way with whatever resources they have at the time.
Oh, and since magic is a thing in the world, then those who imprison somebody in my campaign go out of their way to foil spellcasting of any sort. So a suspected wizard or other spellcaster is usually bound, gagged, and often kept from benefiting from a long rest too.