Any tips for integrating a new manager?

The old manager is moving to another department, and his replacement is said to be very much by-the-book.

Trouble with that is that the book that he is very much by is written from theory, not practice; we the managed have had to develop workarounds and shortcuts and standards that are not entirely in compliance with policy to do our work in a timely manner.

Oven cleaner, for instance. We are provided with Brand A, which is about as effective as Windex. The store sells Brand B, which can take the paint off of cars. We have been eschewing Brand A, instead ‘buying’ Brand B and charging it to the store.
That sort of buying is a common-enough practice, but I don’t think that this new manager is going to be very keen on that.

It would be nice to keep our present setup (there is no hope of changing the rules, alas), but that would require informing the new guy, which would very probably end with bad feelings all around.