The weapon itself is without question smaller than the choppers (Doubly so if there are indeed two projectile weapons installed there along with the sword) and though it's arguable how much power it would take to fire it considering it uses shots, it's also without question that the full power output of the core isn't even slightly necessary just to fuel one of the things. Throw in that the choppers here prove that it only takes 8 of the things can carry a full Jaeger with two plasma shots when we only need one, a bunch of other heavy weapon features, coolant, and EXCEEDINGLY heavy metal parts and armor that a single chopper would decidedly not need means it's entirely feasible that those very same coppers carrying it would be entirely capable of being mobile with the weapons installed, provided it was designed properly.
And as I've said repeatedly, designing something as simple as a chopper with a few tweaks is LAUGHABLY simple compared to designing a giant humanoid robot, keeping in mind we haven't even mastered getting regular sized humanoid robots working on two feet yet, and going bigger would bring all kinds of nightmarish weight problems to the design table. And that's just to start with, before we start factoring in things like ease of damage to the moving parts which brings more weight problems to the table, the power output and fueling each of the individual parts to keep them moving, cooling needs all of which would have to start from absolute scratch (Unless the Japanese had already started like they probably have but that wasn't even slightly said so I doubt it) which is a nightmare in and of itself. And then having to freaking design drift technology and the neural handshake out of freaking nowhere to boot, I wouldn't be surprised if quite a few scientists heads exploded trying to work out all the logistics out in the process of just getting one of the damn things working, not having time for nuclear shielding aside.
And that's BEFORE they also designed the weapons to put ON the giant robots.
That said, the anti Kaiju missiles on the fast Jaeger were pretty small. Laughably so in fact, the fast bot had six of the cannon things, each of them tiny compared to his hands, and I reiterate, the hands are smaller in volume than the choppers in question, least on the main bot and I doubt his hands were much bigger. You could easily, easily install those on current tech without question. Not the full on six for a single chopper probably, but it'd still be damn easy and numbers would easily make up the difference.
As for aiming, the Kaiju are huge and notably not that fast on land, missing isn't that huge an issue when all is said and done. It might miss occasionally, but with enough choppers around a Kaiju at a respectful distance out of easy reach all focusing on firing sort of downward to avoid friendly fire while a few shots might miss the majority should do fine.
The far bigger issue would be dodging any projectiles or abilities thrown at them, which while it wouldn't be hard because thrown projectiles are thrown projectiles and the Kaiju winding up is a massive tell, could still easily would certainly make things touch and go if it flails with the stuff it grabs quite a bit and would definitely bring in some losses to the table in quite a few encounters. However, Choppers are easy to replace by comparison so that's not nearly as big a deal.