Actually, it'd probably be a pretty novel experience playing a game which realistically simulates space combat... It'd become a matter of relative speeds - you're probably already moving at a ludicrous clip, the trick is to dance in and out of range at the maximum accurate weapon range using braking and thrusting maneuvers.... Forget changing direction rapidly, but you could probably do some minor jinking to avoid long-range damage.
The Lucasarts X-Wing and Tie Fighter games had a mechanic which would blend well with that style of combat - namely shield juggling. Assuming you'd allow enough of a fudge factor in your science to permit some analog of a force field, changing the orientation and concentration of a field to deflect incoming fire from multiple directions is a tricky but engaging mechanic.
Finally, it wouldn't have to be completely soundless - remember electromagnetism - assuming hull sensors which picked up and amplified emp and vibrations caused by passing through magnetic fields from shots or engine wake, you could hear a lot of really odd sounds. And as far as explosions, don't forget the stuff that a ship is made of has to go somewhere if it blows apart, and that somewhere is pretty much everywhere. Anything blowing up behind you (movement-wise) would be eerily silent and anything blowing up along your vector of movement would sound like electromagnetic shockwaves and a nasty hailstorm.