Actually, we all wake up naturally at the ending of each REM-sleep period (research hasn't yet found out why). These very brief awakenings are called 'micro-awakenings' and sometimes also occur spontaneously during dreaming. The prerequisite for using these awakenings to do WILD or MILD is to intend, before you go to bed, to remember to recognize the moment you wake up during the night. This way you can wake up without using an alarm clock.

Personal tip: You could also use your mobile phone as an alarm clock but instead on setting it on 'sound' mode, setting in it on 'vibrate' mode. If you risk carrying your phone in some pocket while you're sleeping (or somewhere in your pillow?), you might wake up from it (without the annoying loud alarm sound ringing).