Cordless mouse for hardwareboxing

Got 3 computers currently and would like to try some hardwareboxing. Only softwareboxed so far so its a bit new to me. I'm probably ordering something from Vetra but I also would like to know about mousesetup for handing in quests etc.

If I purchase 3 identical wireless mouses and hook them all to all 3 computers. Will the mouse on all 3 screens move if I move one of the physical ones? Couldnt find any info about this, maybe I search for something completely wrong but some help would be great : )