Thank you for posting your query on Microsoft Q&A.
From your description I could understand that you are looking for a way to export "non-exportable private key" from Azure Key vault.
As per Exportable and non-exportable keys
Non-exportable: The policy used to create the certificate indicates the key is non-exportable. In this case, the private key isn't part of the value when it's retrieved as a secret**.**
Since private key isn't part of the secret, hence it can't be exported. Please do let me know if you have any further queries.
Thanks,
Akshay Kaushik
Please "Accept the answer" (Yes), and share your feedback if the suggestion works as per your business need. This will help us and others in the community as well.