What is quickest, least number of taps possible on Apple Watch to “check-in” with somebody?
Take a look at the Do Button by ifttt

https://ifttt.com/products/do/button

You can create a button/recipe that sends an e-mail or sms to your significant other saying 'I'm Alive' or something.

Then all you ever have to do it just tap the button and the program will do the rest :) So at most it should be 2 taps, 


Open App
Click button to start recipe


I do not have an Apple Watch but it might be possible to do it in 1 if it allows you to add a shortcut in glances or something.