The "it must be a whole transporter because the ship had none" argument sounds hollow because the ship necessarily had dozens if not hundreds of transporters. How plausible would it be for all
of them to go up in smoke?
We know that the ship's main transporters have "bottlenecks": way back in "Enemy Within", it was possible to hit a key set of cables to disable the entire system. But we also know that TNG era ships are likely to have independent transporter units lying about, aboard the auxiliary craft, in science labs and workshops, possibly under the bed of a kid who wants to do exciting experiments in secret from his mommy. It would stand to reason that one of those in combination with a targeting aid would do the same job as a main transporter without a targeting aid, at least after LaForge tinkered with it for a while.
One person doesn't have to die. Both Romulan and Federation phasers were shown in TNG to have the ability to be placed on overload where they blow themselves up after about 30 seconds.
But if we want a plot where one person does
have to die, it's not difficult to claim that an exploding phaser would be insufficient for the job, and only an actual beam, specifically modulated or whatnot, would ensure the destruction of the thalaron device.
The very fact that the thalaron device was so exposed to the environment might be taken to indicate that it was in fact heavily shielded and impossible to hurt with things like ricochets or nearby explosions. An exploding phaser might take out the command center and spew debris everywhere - leaving the forcefield-protected thalaron matrix standing free and unhurt in the middle of the cavity created!