You can change the setting in iOS so that holding the side button on your iPhone won’t call emergency services automatically. Here’s how:
Open the Apple Watch app on your iPhone and tap the My Watch tab.
Tap Emergency SOS.
Turn off Hold to Auto Call.
If you turn off this setting, you can still use the Emergency SOS slider to make a call.
(This how-to is based on my experiences and info on Apple’s support pages — where the images sometimes come from.)
So, we can call at any of the numbers listed?
No. After the watch calls emergency services, it calls the numbers on that list to let them know you’ve fallen, Presumably it also lets them know that emergency services has been called.