We're trying something similar with our project. Where we are mice walking off by themselves is expected to be a problem. So, we are taking the bluetooth hubs with the mice and keyboards. The mice are bound to the bluetooth hub so whereever it's plugged in will be where it works.
Bluetooth has a range of up to 33 ft, so each device has to be paired with another device. That's why you can't just take one mouse from one comp to another. There would be overlap if it was designed that way and you would end up controlling all of your comps at once.
There may be some software somewhere, but I don't know about it yet.
