I don't think you will need to enable promiscuous mode (unless you care about dropped packets as well). If you use a network monitor one of on the hosts you want to monitor, that should be all that is required. You need to be careful when you enable promiscuous mode, it can be hard on cpu resources if you have a ton of traffic.

Depending upon the organization, even enabling promiscuous mode might require change management.

Another idea, assuming your switch is capable, you can bind that machine to it's own vSwitch and physical Nic, mirror the port it's plugged into (at the physical switch level) and put a sniffer on whatever is plugged into the mirrored port. If change management is a big issue in your organization, this one might be harder as it requires changes to the virtual side and the physical switch.