Isolating a Distributed Replay environment
Since the target SQL Server could have a stored procedure using a hard-coded SQL Server account and password to connect to some other server, I'd be unwilling to be 100% certain nothing could touch production unless I had a truly separate network setup to run the Distributed Replay batches against.

One could go to great lengths to try to ensure nothing hits production, but what if you miss something?

I'd setup a bunch of VMs for the controller, replay machines, and the target SQL Server(s), and configure them on their own virtual network, just to be sure.