Read up on "HP Link-5" technology. 1 little USB interface dongle can link to up to 5 devices at once, and the devices are easily changed (they are not matched to a particular Link-5 dongle until they are "paired" to it by the user).
We've been using the specific HP Link-5 mouse shown HERE for years. The batteries in the mouse seem to last almost forever, and HP also has fancier Link-5 mice. You can link any of them to your existing Link-5 dongle. Link-5 is a proprietary HP technology, different from Bluetooth, and there is a brief article on Link-5 HERE .
I have attached a PDF on Link-5 from HP below...