You may be able to "update" the Mouse Drivers from Device Manager using only the keyboard.
Press "Windows key + R" to open the Run box. Type devmgmt.msc and press Enter. Once in Device Manager, press Tab to move into the folder tree. Navigate down to Mice and Pointing Devices, expand the section and move the highlight on to the actual Mouse entry. Press Enter to open its Properties sheet. Press the "Tab" key until the tabs at the top of the sheet are in focus, then right arrow to move to the Driver tab. Now use the "Tab" key to move the focus down to the Update Driver button. Press Enter and you should be able to set it to update the drivers automatically.
...worth a try.