If you use a teleporter to send crewmen, remember as they damage a system the enemy ship loses 1hp in hull damage as well (ruining your chance for the achievement get). Same goes for systems damaged by fire spread.

Your best bet is to get 2-3 weapons that fire missiles, and don't auto-fire them. When they are all fully charged, pause, and target drone system and weapons. The drone might be able to destroy one missile, but the others should hopefully hit.

No, no Stealth Weapons capability as standard

The Stealth Cruiser does not appear to have built in Stealth Weapons capability.

How I tested it

For the sake of testing I upgraded the stealth capability so I had a maximum duration, engaged an enemy, waited until my weapons were charged and then stealthed. Upon first impression it seemed as though Stealth Weapons capability was built in, as I was able to fire both weapons while cloaked without being pulled out of cloak.

However, upon further testing it appears that the duration of the cloak was affected quite significantly once weapons had been fired:

In this image, I activated my fully upgraded cloaking system the moment I heard the enemy fire at me. This was just enough time for all of my weapons to come online, so while the game was paused (and I was taking this screenshot), I targeted the enemy ship with my two lasers and then unpaused the game:

You can see the lasers firing on the screenshot, I only unpaused the game for a brief second before pausing again, and as you can see this halved the duration of cloak. It appears that for each weapon fired about 20% of the overall cloak duration is removed, so if I had fired my beam weapon as well I would have expected the remaining cloak time to be around 30% of its total duration.

Firing the same weapons in the same way with the Stealth Weapons augmentation completely negates this drain on the cloak duration, so I can only conclude that no - the Stealth Cruiser does not have innate Stealth Weapons capabilities.