Consider this, there are risks that you may not even know about!
There could be a pressing legal issue that only senior managers know about that could affect your project. In that case, even you, the project manager, doesn't have this information in your Risk Register.
The answer in your situation is simple. You mentioned that your Risk Register contains
very sensitive information about potential problems.
By definition of the problems being labeled as
very sensitive information, you do not want to make that public.
The analogy I use in this scenario is in Government security. There are oftentimes may layers of security with varying degrees of personnel authorized at different levels. At the top secret levels, the most sensitive risks are known. At the bottom levels, only very granular risks are known.
If you are the maintainer of this document, then you need to work with your managers to identify the level of sensitivity of the risk, and determine what type of
secret clearance project members and stakeholders will have.