Hang on. There's a perfectly good way to keep the mysteriousness of the Shivans.
Tell the story from someone else's point of view.
Keep the individual mission briefings highly specific, something like "Enemies here. We will kill them. Adapt and exploit weaknesses," but have the command briefings and debriefings as reports on what you're doing to the enemy. Something like "The GTD Minnow was destroyed by Shivan forces yesterday in a surprise attack on the Ross 128 node" or whatever with the recommendation being "Hunt. Prey on the interloper."
In addition, to reinforce the alien-ness, you could even name all of the enemy ships variants of things like Prey, Meat, Weak, Opponent (for worthy enemies), Goal rather than the actual names they have. Likewise, your allies could be Pack, Hive, so on and so forth.
Finally, no allied comm chatter, just directives and messages of panic and fear from the enemy. Keep the feeling that you are a terrifying force from beyond space.
I think I want to make this.