I have assigned the wrong driver to my USB mouse, and everytime I connect it the system crashes (BSoD). Now I have to change the driver, but it must be done while the device is offline. Is it possible?
Yes, it's possible but you have to enable the display of hidden devices in the Device Manager.
Once you find the problematic device (its icon will be faded as it's currently unplugged), either update the driver or uninstall (delete) completely the device so Windows will install it again (with the correct driver) the next time you plug it in.
If you want to remove offline devices in Device manager, go to the command prompt and type
This should start device manager with offline/disconnected devices shown and allows you to remove devices.
However, it is possible it will use the same driver automatically next time it is connected, so look in the details of what files it is using and try to delete them (well, the unique ones).
Alternatively, you can also use a tool called Nirsoft USBDeviceW that should show offline devices and allow you to easily delete them.