Decrypt AES Cookie outside of the load balancer

There's no private cert or other similar information, no. The algorithms could be described sufficiently for you to independently write a decryption program, but they are complicated and non-standard. As I said, those details will eventually be forthcoming. If you absolutely need them now, then you can open a support case and they can be provided to you.

 

 

That said, if you're OK with creating a service on the BIG-IP, why not just write an iRule to do that and expose that VIP only to your internal testers?