some wireless aps have somthing called a Privacy Separator. This means that any wireless clients cant connect to other wireless clients.
So as long as one of the wired pcs was running the game server all the wireless pcs would be able to connect to that but not to any wireless devices connected to your wireless ap.
as for damage to the router there is nothing anyone could really do to damage it. If they did get in and screw up the config they usually have a reset button on them!
Edit: good idea ramrod, you are not gonna have to type this password in often so why not make it something silly like 5fg@£rG FS#^& etc