How to destroy AI ships without weapons?

Solution 1:

Sometimes the only winning move is not to play. Jump away if you find an AI ship and try to find a weapon ASAP.

Solution 2:

You can destroy AI ships with only a crew teleporter. The key to that are the following facts:

• Whenever you completely destroy a ship system, the hull will suffer 1 damage
• AI ships have an augmentation that auto-repairs damaged systems.
• A level 2+ crew teleporter will recharge quickly enough that you can save 100 HP crew before they die from suffocation.

If you teleport crew into an AI ship, they will start suffocating immediately because there is no atmosphere. However, as mentioned, you can save them before they actually die, either from teleporting them back, or by using the "healing bomb" (it can miss, so have a level 2 teleporter ready just in case). Until you have to recall them, they can deal system damage. Heal your boarding crew and repeat until the system is destroyed and the enemy ship suffers damage. While you wait for the repair to happen, rotate through the other rooms. Always attack the most recently repaired system, because it takes the least time to destroy again. That way, you should be able to destroy an AI ship with only boarding crews.

For finishing off the last point of hull damage, you can either sacrifice 1 crew member, or use a boarding drone. Note however that a boarding drone cannot die to suffocation and thus cannot be re-deployed in an AI ship, so you must not use it before dealing that last point of damage.

Obviously, the AI ship can still damage you in return, and it will take a LONG time to destroy it that way, so it's most likely not worth bothering. But it is very much possible in principle.