Turned out that in that case, you have to leave the shield drone off and only use the anti-drone. The anti-drone does not always kill enemy drones (sometimes just stuns), and after depowering/repowering takes an oddly long time to acquire a target and shoot again.
The enemy has a beam weapon? So do you, so shoot theirs! They should only get one shot, and if it hits anything other than your weapon or drone system, you're fine. And quite a few enemy ship layouts - especially auto-scouts - have their weapon and drone systems adjacent so you can hit both with your one beam shot.
Or finally, the other answer is, yes you do take a chunk of damage from such a fight. I had one that dealt 7 or so. That was survivable.
The enemy has a beam weapon? So do you, so shoot theirs! They should only get one shot, and if it hits anything other than your weapon or drone system, you're fine. And quite a few enemy ship layouts - especially auto-scouts - have their weapon and drone systems adjacent so you can hit both with your one beam shot.
Or finally, the other answer is, yes you do take a chunk of damage from such a fight. I had one that dealt 7 or so. That was survivable.