I would like Akamai not to cache certain URLs if the origin server sends a specific header. Is this possible to do with Akamai?
The question has been covered pretty well here: Bypass specific URL from Akamai if certain cookie exist
I would be surprised if there is no build in way to do this. In many cases, it is too difficult to configure these rules in Akamai. Only the origin server knows when a page cannot be cached.
If you are using Property Manager, you can do this with the Property Manager API or in Luna.
The Property Manager API documentation is here: PAPI