Well you're going to have the switching device issue regardless of whatever solution you go with. An HDMI cable from every PC to a HDMI switch would be pretty easy and just set all of the PCs to mirror on their second screen.
I'm sure there are professional grade, and very expensive solutions that would allow you to split the screen 4ways with 4 inputs but I don't know how that would be superior to just switching the inputs.
Get an IR remote controlled switch. If you want everyone to be able to share on the big screen without getting up just buy 3 additional cheap leaning remotes so they can change the input.