bleh, it's a gravedig, but since everyone is playing stupid I'll put a plain answer here for anyone who -doesnt- know by now.
Go to your freelancer shortcut (usually on the desktop unless you're weird). Right click it, select properties, then go to the line in the window that says "Target:" and has the shortcut location. At the very end of that line, after the quotation marks at the end, type -nohud and apply. Whenever you play the game now, the hud will be completely gone - nothing at all on the screen except space, not even a cursor from what I remember, though i havent used it in a while.
To elaborate on the above post, basically everything is gone except your ship. In order to record good videos, you should go into cockpit view (CTRL + V default). Remember that all that you'll be using in -nohud to navigate are your hotkeys.