FIRST THINGS FIRST: HOW RELIABLE DOES IT HAVE TO BE?
First, it should be noted that pretty much any Zwave device sold has a manufacturer's warning that it should not be used for medical equipment or other equipment required in an emergency. The reason is that while zwave and zigbee are both reliable enough for most home automation uses, The nature of mesh is that occasionally A message may be missed or delayed. You don't want to bet your life on it.
Also remember that smart things is a cloud-based system. If your power is out, or your Internet is out, or your smart things cloud is unavailable, you will not be able to send any notifications.
On top of that, the smartthings platform has issues with reliability. The company has acknowledged that (as you can see from the many threads in the forum about it) and has made improving reliability a priority. But they're not there yet. Just this last week there was a system outage of several hours.
When smartthings works well, it is absolutely my favorite home automation system. But I use an entirely separate system for security and for emergency alerts of the type that you describe. And the system that I use does not require the house power or the Internet to be available – – it has its own cellular notification system.
I do use smartthings for noncritical alerts, like notification that the guestroom window was left open when rain is expected, but personally I wouldn't use it for any emergency notifications.
OK, that said, it's very easy to send notifications from SmartThings. It's actually one of its strongest features.
There are several customs smartapps that can do exactly that. "Notify me when" is a popular one available under the marketplace tab in the smartthings mobile app. Look in the Security section.
If you have an android phone, you can do it with a combination of sharptools and Tasker.
And the easiest way which works regardless of your phone type is just to use IFTTT, which is a free service that works with SmartThings.
CHOOSING A DEVICE
There are a number of devices that can be used as buttons with smart things, including a zwave panic button sold for just this purpose. See the following:
Personally, I would consider going the other way.
I really like the flic button. This is a rubbery button about the size of a quarter with three options click, double-click, and hold. It has its own app which lives on your phone. It has an adhesive on the back so you can stick it on to anything. If you buy at Amazon it costs about $35, if you buy it from their site you can get a bundle pack of four for $99. (The early ratings for the flic were terrible because of a software bug, but they fixed it pretty quickly. So read ratings from 2016 and newer.)
This has an IFTTT channel which means you can use the flic button to trigger smart things events like having lights come on or a siren go off.
On its own, it can also send a text message.
So that's what I mean by doing it the other way around. Instead of having a SmartThings device trigger your emergency response events, you have the flic button do the emergency response and then double-click it to have smart things do stuff. My personal belief is that this will be much more reliable than SmartThings. For one thing, it's a point-to-point protocol, not mesh.
The biggest downside to the flic is that it must be within about 30 feet of a phone or tablet that has Internet access. It can't access the Internet on its own. At our house we use a tablet as the home automation control center, and we pair the flics to that. If you're going to pair it to your phone, the flic will not work if you take the phone away and leave the flic behind. So that's just something to consider. It will work for some people, but not for others.
So there are multiple options, it just depends on the exact details of what you want to do. And how reliable you need it to be.