The corporation acquired us to provide engineering support for their product while actively maintaining external contract projects.
I am literally swamped with external work ... but it seems that every other internal project is of an "utmost priority" and everything else has to go aside.
The picture I get is that actually they acquired you to provide engineering support for their product. The fact that in doing so they had to take on your contractual obligations appears to be treated as an unfortunate side-effect, although of course nobody turns down the money when it's due.
You're overworked, especially with this extra two week job taken into consideration. Of course you want to drop the task that's least appealing to you, especially in view of the fact that there exist cheaper, trained people perfectly capable of doing it. That's not how it works though, you should drop the lowest-priority task given your company's actual situation, not the situation that it would be in if they'd taken your advice in the first place and hired that cheaper person a month ago. They chose not to replace the PCB tech (certainly not as a matter of urgency), now you and they together will deal with the consequences.
- if your boss is aware of your workload,
- and your boss, not you, bears responsibility for servicing the external contracts[*], and realises that this is an either-or situation, you can't do both at once,
- and your boss is aware that someone could be hired (perhaps as a contractor?) to do this job, cheaper and quite possibly faster since they're a specialist at it,
- and your boss nevertheless determines that this is your highest priority,
then you do it. And if (for stupid, frustrating reasons that you could have predicted and prevented if you'd been in charge) you're the only person available to change a light bulb in the office, then (health sand safety permitting) you change the light bulb in the office. We're professionals, we're specialized, but we don't have to be precious about it.
Unless you have a pretty good understanding with your boss (it sounds like you don't) then in this first instance you should not convey that you won't enjoy the task. That's irrelevant, it still needs doing, and if everyone were completely candid then satisfying your preferences might not be his favourite task either. Do the task first, then maybe say it sucked afterwards if you think it'll do more good than harm to say so.
You should convey to your boss that you're currently a bottleneck, and other projects are at risk too. That's basic professionalism and it's the information your boss needs to prioritise. By all means suggest that this (and perhaps a list of other things) would be relatively easy to shift off you. If you make that list of other things then be honest, include in it things that you enjoy but that other people could do.
Longer-term, if you don't like the job any more (as it develops under the new management) you can say so, and if there's a pattern of assigning you tasks that don't require your particular education then you can raise that as a problem: both that your manager isn't getting the value he should get out of you and that you're not able to develop in your field because you're working on other tasks. For one crisis you can't be straight onto your high horse. For the tenth crisis with no improvement, sure you can, because by that point the job as it stands isn't looking like a good one for you any more.
Btw, the fact you're such a critical bottleneck is in itself worrying. If you got hit by a bus and spent two weeks in the hospital, quite possibly you wouldn't have a job/company worth coming back to under these conditions, and your new company would have wasted whatever it spent on the acquisition.
[*] If you carry the can for the external projects, that is to say your boss is making a request without considering truly dire consequences, then you can and should push back hard. "If I do this, I take two weeks out of my usual work, we break contracts we're committed to, we'd get sued. I can't just agree to do that, we need absurd amounts of authorization to abandon these contracts even just for two weeks". Again, the fact it's beneath you is completely irrelevant. It could be the most perfect use of your abilities ever, but if you're committed to other things then you'd have to let it go by.