Does he want to cover his ears or leave the situation, or does he just get mad?
He covers his ears when it's very temporary, like sirens. He leaves the situation if it's prolonged. He doesn't lose his cool in public. If he can escape, he will. It's usually when he's stuck at home (landscapers) or can't go anywhere (3am in the morning, trying to sleep) that he gets mad.
I don't think testing for ASD would be useful - it doesn't change the symptoms or reaction, and it's not as if a diagnosis would help him get services as his age (or would it??). I do think it's worth thinking more about his reaction to his discomfort, and possibly looking into therapy, especially if you want children but also because it's just not a nice thing to lash out at people/things/situations for something like this, but no diagnosis should be needed for that. How has your husband reacted when you've spoken to him about this? He obviously understand he has an issue, which is great, but what does he think should/can be done about it? Is he willing to go to therapy? Would you consider saying he needs to go if you want to have children?
I agree an official diagnosis isn't going to help that much. He's going to be 34 soon and it's never really affected his life up until now. (I mean, it would if he wanted to do something more public-facing, but he doesn't, so....)
He is willing to go to therapy, but he doesn't want to go to something branded "anger management therapy" since he's afraid it'll show up on his record somewhere. I know he'd refuse to take meds. He's one of those men (IMO, your typical man) who only gets help when he can no longer help himself, so he's going to try meditation and trying harder first. As I mentioned, he also gets overwhelmed easily, so today was just planting the seed. Need to wait a few days to set the stake, so to say. He's already better than a lot of men about self-improvement. My mom was pleasantly surprised he agreed to a pre-marital communication workshop, cause my dad would have refused.
Generally, I'm more "aware" of things than he is. He explained today that he gets mad at Mickey because Mickey yowls even when he has food, water, litter box, and I'm like, "...you realize babies can cry and kids can tantrum for no rhyme or reason either?" It seemed to finally dawn on him why I was concerned.

He expects things/people to make sense and act rationally, and gets overwhelmed and upset when they don't. That's why he can't stand office politics, although he's going to try working in-house for the sake of a steady paycheck, so we can expand our family. I'm a MUCH more empathetic person than he is (I've been told I'm a highly empathetic person in general), so that stuff doesn't bother me at all. Which would normally assign me the role of working parent and him as the SAHP, aside from this issue.

Again, it's not that I'm afraid he'll physically hurt the child. It's me worrying about him handling the stress and not wanting to make life miserable for him, and for me by extension. I can already picture him grumping around 24/7 if he hasn't had a solid block of time to work and/or sleep. I can handle it when he needs to cool off for a few hours once every few weeks, but if every single day is going to be him stressing out or trying to cool off, I don't think I could. We can't be a good team that way, in marriage or parenting.
Heck, I should probably encourage him to get therapy for the work stuff in general. The last in-house job he had, he quit after a week because the code was so awful he had a panic attack looking at it.

Definitely not a normal reaction, but he's been very lucky to have a highly in-demand skill and works extremely well remotely. He's never been forced to face it before, but the prospect of not having enough money to raise a family here might do it. The cost of childcare here in LA is
astronomical. He talks about moving, but we're getting quickly priced out of everywhere else he deems acceptable. Plus my current job is in the local government and I might try to be more influential here, so moving might not be an option with that. And if we moved, it would be better to move closer to our relatives, and all of our immediate relatives are in the Bay Area, which isn't any better about cost of living.
I am diagnosed with ADD - it is very common for people with ADD to be very sensitive to noise because they cannot block out distractions.
I love loud constant noises like a hair dryer or a vacuum cleaner. It drives my husband mad but if I really want to relax, I sit in the kitchen with a coffee and the blasting kitchen hood. Heaven for me since it drowns out the other (for me) annoying noise. I do that to destress.
the noise mostly bothers me when I am already stressed. Is that the same for your husband?
Btw - it is also hereditary for me. My father was/is the same way. He has three daughters and children have seldom been an issue for him as well.
The noise does bother him most when he's working or sleeping. I've learned not to take it personally when he ignores my affections while he's working. He HATES the vacuum. Wears the giant noise-cancelling earmuffs even when he's the one vacuuming.

He reacts to it like the landscapers. I don't think he's the one with ADD -
I would be the one with ADD, if anything. (Easily distracted by fun internet things, energy off the walls sometimes, don't need much sleep. But I can focus enough to get work done, and I can get sleep.) He focuses very well, but I suppose it can't be easy if he has to force out the noise and stimulation to do so. But he's not nearly as distractible with other fun internet things while working, as I am. He's the perfect remote worker.