The usual dc-dc modules...
These will most likely have a counterfeit LM2596 because they all do, and garbage quality capacitors. They will probably not deliver a stable 5V at the rated current and when the capacitors die, output voltage can go over the set value which will fry your alarm. The ones I tested had a fake LM2596 that ran at the wrong frequency, which saturated the inductor, the caps were burning hot due to being too cheap, then died, etc. It's just trash.
Anyway. The peak voltage of 29VAC is about 40V so if you use your AC-DC module you should check the black cap on the left has at least 50V rating, otherwise it will pop. It says it has a LM2596HV which is good to 60V, but who knows what's inside that chip. National Semiconductor was bought by TI in 2011 so if the chip has the National logo on it, at least you can be sure of one thing, it sure didn't come from the official manufacturer!
You can know if yours will die quickly by putting a finger on the caps: if they're warm, it will die.
Here's what I would do...
Locate the source of 29VAC, there's a transformer somewhere. Since you no longer use it, might as well remove it.
If the wires are good for mains voltage, and there isn't other stuff using 29VAC wired to them, then you can just reuse them for mains after replacing the transformer with wire nuts. Now you have mains where your alarm is.
If the wires are in a conduit, you can pull them out and install mains rated wire instead.
Otherwise, I'd replace the 29VAC transformer with a 12VDC power supply, and near the alarm, a 12V to 5V converter that isn't a counterfeit LM2596 module. For these, the highest chance of it not dying due to garbage quality capacitors is to buy one without electrolytic capacitors. If you can find a fixed 5V one without potentiometer, that's another failure point removed. Example, and another from a proper brand. Suggestion: a car cellphone charger, that's 12V to 5V...