And that’s cool. So here’s how you do it.
Go to the Sleep screen, where you usually set your time to wake up window.
Swipe to the left. Just continue, until you can’t no more (like two swipes away). You’ll arrive to a screen where you can start a sleep session with no alarm. If you press Start here, Sleep Cycle only listens and analyses your sleep, but won’t wake you up.
As you wake up on your own, stop Sleep Cycle in the normal manner, as you always do. You’ll get the night’s analysis, without the alarm waking you up.