Wireless / Bluetooth with a detachable mic probably isn't a thing, as then you'll have two devices to pair. I've only used BT headsets which pair as a single device.
You want staff to share the headphones but have their own mic? Is that for hygiene reasons?
I wouldn't want to use shared headphones or a mic. Using shared keyboards, mice and chairs on hot desks is bad enough.
Will they always return to the same computer? If not the headset will connect to the last computer if it's in range and if someone is already logged on to this other computer, their audio may switch to the wrong headset.
Would be easier and cheaper to use wired headsets, no worries about charging, connection issues etc.