I am currently flying the Nesasio without adding shields. The point I come unstuck is when I encounter the flag ship the 2nd time. The drones and power surge are the death of me as I can't keep cloaked or recloak quick enough. I was hoping to be able to swap out the Long Range Scanners for the Weapons Preigniter before the Last Stand, but it was not available in the nearby stores. If you have taken out the Flag Ship with ship without shields, I would be interested to hear what ship and how you did it.

i have not tried a run completely without shields, however, speaking of the drones and power surge, keep in mind that your best bet is using cloack with only one power bar
5 seconds are enough to avoid the barrage, and the sooner the cloack vanish (it can't be manually stopped) the sooner it starts recharging.
You should also master the timing of activation... don't wait for the drones to show up, engage the cloack after 1-2 seconds from the warning; if you do it right, you'll manage to stay cloacked long enough to avoid most, if not all, the attacks while gaining 1 second for the next recharge

I'ts difficult to come completely unscratched, since i'm under the impression that, about mid-fight, there are a couple of surges that come faster, but if you can survive those, the rest won't bother you.