I use 100 pocket display books, these are about 50 mm thick and give you 200 display pages on A4 paper, I get these in England from Ryman office supplies.
I print 2 column per page, print on both sides (My printer automatically prints both sides saving on paper) it is possible to get 100 titles per page side if you juggle the margins down to minimum and set the column margin to minimum as well.
For all this you could only get about 20,000 songs per book maximum.
From my experience, the large lever arch files that you could get a lot more songs listed in, is that they can tend to spring open and the pages go everywhere
So my suggestion would be to either not bother to print a book if you have 100,000 titles as there can't be many requests you wouldn't have
Other than that just print a selection of about 15 - 20,000 so that there is a selection for them to refer to but tell the audience if they can't find what they want just ask.
