That was an excellent suggestion and I'm almost there. After looking up the canonical name for the Network And Sharing Center here, I disabled access to the NetworkAndSharingCenter.
This is great, however, it also disables access for the Admin account also so I'm going to look for a way to only restrict non-admin users. It also may be a bit too much to restrict access to the whole center. I was really looking to deny access to the Manage Wireless Networks page.
There's a way to do it per user, but I'm afraid I can't recall how. I'll dig into it once I'm fully back at my desk (at remote location, doing a repair at present).