I'm afraid not. The panels go away when you deselect units (by left-clicking on the ground) but that won't really help if you're trying to issue a move order. Another option is to open the console with the tilde ~ key and typing 'hidegui on'. This is good for screenshots, but again, not too useful for issuing move commands, since the panels are still technically there, even though they're invisible. (Note: If you use this command, the GUI will return the next time you open the console.)