The thing worth reminding at this point is that there's three very different weapon families in this game: 1) projectile weapons that damage hull, 2) lasers that damage devices, and 3) energy shells that deplete shields -- and hull damaging weapons are generally waste of energy while the shield of an enemy is on, while shield depleting weapons do no other harm at all, and lasers can't do hull damage either, but they work through the shield (at reduced damage, but it does little difference, to hit the exact point at exact angle is the hard part).
So, there's two options how to deal with enemy shields: try to deplete them with energy shells, or try to destroy the shield generator with lasers.
You have 2 energy shell weapons, one heavy and two light lasers available before this mission, but, Angelwing can clone devices that had ever been installed on it, so the count actually doesn't matter: normally you install one of a kind, accept changes, then right after you can have as many copies of that thing as you wish, as long as Angelwing is considered. (And the original is lost for other ships in your fleet, so putting multiple of rare thing on Angelwing while it counts is a huge waste.)
You don't need datascanner for this mission, nor next two (it's needed again for optional objective at the Raptor's base), so, I would go either 4 energy shells, two guns, or 4 heavy lasers two guns. Imho, you simply don't have weapon capability to carry all three types all the time, and you eventually need some guns.
With energy shells, concentrate fire with Chrome, with lasers you can go on your own, but it's a bit more of a game of luck, and Chrome may not survive on their own.
Ah, and don't forget lasers generally don't hit anything unless you have at least one device designated as a target. And, of course you only can target devices that you have detected...
Still, on "professional" difficulty I forgot about energy shells altogether and went all lasers and later gunboats. It seems messy with smaller targets, but makes a lot more sense than trying to deplete a shield of a battleship.
Giving the "damage devices" command seems to sometimes have more reliable results than just aiming lasers manually, they sometimes annoyingly don't fire (I then try to spam navigation points (with 'N' key) and move slightly away from the target ship to approach at different angles.
Btw, engines are the easiest thing to hit (especially from behind) and among first to get detected and crippling enough to consider aiming at even if the original intent is different, also, don't forget to target flak first with or even before you launch gunboats, and targeting weapon generators is generally faster than silencing guns one by one.
