The analysis needs to stand back and apply first principles.
You have a spaceship sitting, minding its own business, in space. It gets hit by a weapon that blasts it with very high energy particles. (Could be anything, bullets, big rock, sci-fi accelerator weapons, very high energy photons, whatever.) The spaceship has a shield system that surrounds the ship and absorbs the energy and momentum in a form that is not dangerous to the ship.
OK, the blast - energy, mass, momentum, can be modelled as a single entity - since it is channelled by the shield system to the generator. Thus we can model it as a moving mass that impacts on the generator. And the ship can be modelled as a single system, it has a total linear, and total rotational momentum, with a given total mass. Thus we can apply simple conservation laws to the system comprised of the equivalent blast mass, and the ship. The total momentum (of both kinds) is preserved. It doesn’t matter what sort of amazing mechanical wizardry is inside the ship, you can simply lump it all together and observe it as a system externally. And the moments are preserved.
For instance, say the blast was perfectly symmetric about the ship - i.e. concentrated on the ships exact centre. If you had the shield generator in this position, and mounted on a flywheel, the axle for the flywheel must be off centre in the ship. As the flywheel receives the impulse of the blast it will begin to rotate, but this rotation only occurs because there is an opposite force from the ship against the axle (otherwise the generator would simply vanish out the back of the ship) and thus the axle imparts a rotational torque onto the ship. And hey, look at that - the total angular momentum is preserved. Not only that, but the impulse also transfers the linear momentum to the total system via the axle. Which is where we came in. You can’t convert between rotational and linear momentum in a closed system. And here the blast and ship together constitute the closed system. You can add another flywheel, and apply a torque to it, so the ship as a whole stops rotating, But the system still contains the total angular momentum, And you can’t get rid of it in a closed system.
The clue about how to get past this is the closed part. If you are able to accelerate mass (i.e. rocket engine) you can eject fast moving mass, and you are no longer closed. So you can dump momentum. Angular stabilisation of many satellites is done in just this manner. Reaction wheels are motor driven to take the momentum from the satellite. However eventually they saturate (i.e. the mechanics of the system can’t cope with making them spin any faster) so they are desaturated. Usually you brake the wheel - which transfers the momentum back to the satellite, and by using a tiny bit of fuel through an attitude control motor you torque the satellite to compensate. It is the mass leaving that allows this to work. The HST can’t use rocket motors - due to the risk of contamination - so it uses electromagnets to hold itself against the Earth’s magnetic field whilst desaturating, and thus it transfers its excess angular momentum to the Earth.
This neglects the question of where the energy went. One assumes the equivalent of an inelastic collision.
So, the overall point remains. If the blast is so powerful that it delivers an impulse that will tear the shield generator out of its mountings and damage the ship, there is nothing that mounting it on a wheel will do to help. The momentum will be conserved, in all forms.