For what it's worth, I think deciding to put things in place unless someone objects within 24 hours is a bad operating procedure, in general. On the otherhand, this has obviously taken more than the 24 hours you stipulated, so what do I know?
Is missing out on sales worth having an exact count of what is sold? If people come in at night and want to buy, they will not always come back the next day. Sometimes they cannot come back because they are leaving town, etc.
My feeling is that we should let night managers know about the system, but not worry too much if they forget or can't figure out a sale some night. If they remember the key, they will remember the book. But why assume none of them will remember and therefore restrict the hours? Most of the people who read the bb are night managers, and I think they are all capable of handling a sale after the KMs leave.
The book is a good idea, but there is no reason not to let a NM do a sale if they remember how to. To my knowledge we haven't had any problems with that particular key going missing, or anything going missing from the locked cabinet. Implement the book, put the key with the book, and we'll add the details onto the NM letter.