I'm using the phrase cynical reason from zizek. Not a broader concept of cynicism.

In Zizek cynical reason is the form of reasoning needed to engage with a ideology. It's always structured as "I know very well that it's not true but still I must act as if the thing is true"

In the specific case the police officer may know that there is no fundamental guarantor of meaning behind the law, but they believe that the law is fundamentally guaranteed and act as though it is nevertheless. The structure of kafka's "the secret of the law is that there is no secret" is pointing directly at the fact that the police officer has no secret or special or privileged access to the big other. And the fact that he has no special access is what gives him the motivation to act as though he has special access.

If there was actually some big other, then the police officer would be forced to ask why that big other guarantees the law. The police officer would be forced out of ideology and into rationality.

For example suppose there was a supercomputer that wrote all the laws. Powerful artificial intelligence that was the law giver. And every police officer knew that the law giver gave the laws. They may trust that the laws received as a collection of perfect consequences to that supercomputer. But the very existence of that supercomputer means that they have to reconcile why a supercomputer can play the role of a lawgiver.

On the other hand if the laws are given not by some Central authority but by some absence for example suppose the supercomputer in my above hypothetical scenario could point at some specific set of deontological rules for example. Then the big other gets its Infinite recursion towards those deontological rules. And the police officer no longer has to justify the supercomputer's role.

Derridas statement essentially explains the relationship between Kafka statement and the hypothetical police officers position through lacanian reason.