As you noted, there are two resources needed for most ICSF CCA callable services: CSFSERV and CSFKEYS.
I mention that because I wanted you to be aware that CSNBSYE is one of a small number of services that don't require access to a CSFSERV resource, only CSFKEYS.
Though not directly related to your question, I also want to clarify what you mean when you asked about "hash & sign a message," but then referred to CSNBSYE, which does neither of those things.
All that said, I am not a CICS expert, but my understanding is that there is a way to accomplish what you are asking. I'll reach out to some CICS folks and see if I can get an answer.