At least one of the missions that require scanning asteroids can be completed without firing a shot... I've done it twice. now.
Be creative... if it says you only have to scan to complete the mission, crank up the engines and figure out how to zip or sneak in and get your scan without having to fight.
I used a speed power setting and approached from a high positive or negative position on the z-axis under full impulse, slowing when I'm almost on top of the asteroid. Get the asteroid between me and whatever nasty is there guarding it, scan... and if they haven't fired yet, hit full impulse again. if they have fired, hit evasive maneuvers and bug out. If you aren't moving fast enough yet, pop an engine battery as well.
Once or twice I was fired on before I could complete the scan. If you're close to the asteroid and the enemy is a big slow ship, just position yourself opposite the bad guy and re-scan.