Ok, but you'll have to sacrifice a penguin first. Just joking.
Maybe just "freezing" all the applications that allow recovering those data, it is, do very strict chmods to du, top, memstat, the whole /proc tree, etc. If the user can't run the commands or access the data then most probably can't find out anything about the hardware.
Of course there are still perl and company where the user is able to install its own scripts. If some script needs data from /proc it'll bomb and your user may get angry. I'd study first the possible consequences. Maybe not the whole /proc needs to be blocked; I've just pulled this answer out from the magic horned helm, more analysis is required.