What you are describing is the "alternate screen" feature that some terminal emulators have. The linux virtual console, for instance, doesn't have this feature.

not leaving a trace in your terminal.

Actually this is not 100% true. In xterm you can find "Show alternate screen" in the menu that opens when you hold down Ctrl-MiddleButton. Even after less has been quit, xterm still shows its display (of your secret files) in the alternate screen.

Update: Regarding your question how you can do this: I think that ncurses (which "less" uses) does this by default when you initiate the screen, so you should be able to do this with the Curses module (as atcroft suggests).