Any mouse regardless of brand should work as a basic mouse (ie 3-button functionality) without external drivers. They're usually only required to support the extended/non-standard features of a particular mouse in my experience.
You may need to reboot your laptop with external mouse plugged in, try that.
Or maybe the touchpad has to be disabled.
On my laptop I don't have to do either of those things, but not every laptop behaves in the same way with external hardware.