Creating A Secure Wired Network Alongside A Wireless Network?

I have been involved in the Networking of a museum with a set of "Show" computers which display video, and for this reason cannot have anti virus installed becuase of the performace hit, and also the risk of pop-ups on the videos. They do however need to be connected to the internet as some are interactive and allow people to send simple emails, and they all need to allow remote support when things go wrong.It seems the networking was not thought out very well initially, and there is a single wireless router which serves the staff and public on a secured wireless network, but also serves the "Show" machines via a wired connection from one of its ports, which then connects to a master switch which serves the show machines.Now the wired and wireless is on the same network, and everything shares the same IP subnet (192.168.1.xxx), and this is not a good situation in terms of the securuty of the show machines on the wired network. So I need to work out a way to totally separate the wireless network (which will be very prone to people opening viruses in their emails etc), from the wired network (which will be the show machines which wont be touched by anyone).

I want to achieve this in the simplest and easiest way, and have been reading about the possibility of setting up a second wired router behind the current wireless one, with a different subnet IP address, to which the "Show" machines could be connected. The WAN port on this second router would connect to a LAN port on the wireless router, and thus the show machines could get their internet, but separated from the dangerous wireless network.Does this sound like a sensible start? Will the fact that the wired router (and show machines) are on a completely different subnet to the wireless router (and wireless devices), mean that the wired network will be protected? Or do I need to do more? And is this likely to work?