And that works, too! Here’s how you do it:
Go to the Sleep tab, where you usually set your alarm.
Swipe to the right twice. You’ll arrive at a screen labeled 'analysis only' where you can start a sleep session without an alarm. If you press "Start" here, Sleep Cycle only listens to and analyzes your sleep but won’t wake you up.
When you wake up, stop the Sleep Cycle app as usual. You’ll get the night’s analysis without the alarm waking you up.
If you have an Apple Watch, you can also do this by using the automatic tracking feature; you can read more about the Apple Watch integration here:
https://support.sleepcycle.com/hc/en-us/articles/206704349-Sleep-Cycle-and-Apple-Watch-Integration