Is there a way to do fair exchange between two parties who don't trust each other?
I think what you want to look at is "fair exchange".  There's a giant catalog of protocols for fair exchange.  They've been designed for doing exactly what (I think) you want.

See, e.g.,


https://en.wikipedia.org/wiki/Multi_party_fair_exchange_protocol
Alice trusts Bob only when Bob trusts Alice


Some fair exchange protocols require a third party who Alice and Bob trust, and involve the third party in the protocol.  Others (called optimistic fair exchange) require that there be a trusted third party, but normally the third party does not have to be involved in any way -- the third party only gets involved to settle disputes, if something goes wrong.  Still others try to avoid any third party (e.g., gradual fair exchange); they're not perfect, but they try to ensure that if Alice can learn Bob's message with some amount of effort, then Bob can learn Alice's messages with not too much more effort.

To learn more about fair exchange, do a literature search on fair exchange.  There are lots of research papers on this topic.