Can you activate a system where you have no units and not move any units?
You can (barring an rules reference update by FFG).

The rules on Tactical Actions have the following restrictions:


  The active player must activate a
  system that does not contain one of his command tokens.
  
  • To activate a system, the active player places a command
  token from his tactic pool on that system. That system is the
  active system.
  
  • Other players’ command tokens do not prevent a player
  from activating a system.


As noted in the question, moving ships is not a requirement of the movement step of tactical action.  Nowhere in this are you prevented from activating such a system.

Three things to note if you are doing this to get a space cannon volley:


You will not be able to subsequently move units into that system this round (unless you use the Warfare strategy ability) as it already has one of your command tokens.
You cannot do this if you have already activated that system this round (unless you use the Warfare strategy ability).
The only space cannons that work with this are your own (see this question for details).