Never plug in or unplug a mouse connected to a PS1 connector while the system is running. A second mouse is fine to plug in at anytime as long as it is USB. Installing the driver for the second wired mouse should be fine, the sytem will install the driver when you plug the mouse in to the USB connector.
If you open your Device Manager and check the driver version of each mouse and they are both using the MS Intelipoint driver you already have installed, perhaps both would use a later version of the intellipoint driver you may install. If the new USB wired mouse is not using the same Intellipoint driver as the wireless mouse with driver already installed, I don't know. Two Intellipoint drivers for two different products may cause a problem. You can always uninstall any driver you load up from the Device manager or the Add/Remove programs.