I'm amazed at how people behave regarding their neighbors and little, petty annoyances. It's a noise, for pete's sake, and it only happens a few minutes before you're going to get up anyway. Is it really that big a deal that you have to go SAY something to the neighbor about? Do you complain to the city because the sound of the bus roaring down the street wakes you up, or the garbage truck interrupts your downey slumber? I've experienced these things, and learned to accept it as part of the cost of living in the place I chose. It's a city, cities are noisy, if you're beyond coping then get yourself some earplugs. or move.
Alright, let's say the noise is "different" than normal city/apartment noise and you just really need it to stop. You go talk to the neighbor, and you use words like "well, it goes off while we're trying to sleep, and could you maybe move it away from the window so the noise won't wake us, or put it on a softer setting, or shut it off promptly? That would help us get better rest and we'd be very thankful. We really appreciate it..." You don't use words like "hey, could you shut that f*'n thing off when it goes off, you're waking the whole d*mn neighborhood, we really don't appreciate it". You talk about it, not gripe about it to them. Twice should be enough, doing the same thing both times, not escallating one iota. After that, it needs to go in a written letter to the landlord documenting the problem, the times & dates you talked to them about it, gently explaining that you've tried twice to resolve this and need to come to some kind of understanding. That's right, you don't threaten anybody, you don't say "I'm angry", "I'm upset" nor even "I'm frustrated", you just ask for dialog on the subject. Sorry if that doesn't sit right with your testosterone, but that's how civilized people do things. That way, when some s*thead (who happens to resemble you in some vague generic fashion) who's ALSO fed up with the disturbance sprays a hose in the window in protest, you'll be credible when you say "no, I talked to her quite nicely about it, twice, and sent a calm note to the landlord, I don't resort to petty vandalism to address issues, there are better ways to handle a situation".
Maybe you did all this, and things still happened like you described. Even if the wild-eyed guy showed up at your door with a golf club threatening you, you can still head trouble off at the pass. He was probably more worked up over the fact he couldn't get you in a dialog. Maybe you could have said "Look, pal, you seem pretty worked up. I would be too, if someone did that to me. But I didn't do this. I had an issue with the alarm and we talked about it like decent human beings. I'm not the kind of person to do that, and I'm telling you I didn't use a hose to get satisfaction. I'll be happy to meet you down at the corner Starbucks in 15 minutes to talk about this like decent people if you want. A few extra minutes of shut-eye in the morning is not worth losing a good neighbor relationship over. Maybe if we think about it we can figure out who did it."
Wouldn't have showed the gun. Wouldn't have called cops. Personally I think you did nothing WRONG but there were a few things you did that could have been a little more RIGHT. You were within your rights on all counts but I would have played it a little differently and (perhaps thanks to the way I do things) I've never lost a good neighbor relationship nor had a crazy man with a golf club on my stoop threatening me.
I just had the thought that perhaps her alarm goes off for an hour solid is because she spends the night at her boyfriend's house on the spur-of the moment and forgets she has the alarm set at home. My alarm repeats every day unless specifically turned off, and it sounds for an hour - sounds like hers is the same. We had a roommate who went away for a week and forgot and left his alarm set. We went to the circuit breaker on the side of the building and flipped switches until the alarm quit sounding, then left that switch off until the day before he came back. Nothing was ever said... glad he didn't have a fridge or tropical fish tank on the same circuit!