How to use a selfie stick without a remote control: Take selfies using a self-timer
The best way to take a selfie without touching your screen is to use a self-timer feature. Phones running Android KitKat or later and iOS 8 have this functionality built-in, and you can specify either a three- or 10-second delay. There are also plenty of free apps in Google Play and the App Store that offer self-timer functionality.
The alternative to using a self-timer is to use a gesture (with the arm that's not holding the selfie stick, of course).
How to use a selfie stick without a remote control: Take selfies using gestures
If you're an iPhone user you should check out the GoCam app from Crunchfish in the App Store. It's free and lets you capture selfies from up to 10ft away using a simple hand movement. Check out the video below to see how it works.
CamMe is a similar app for iPads and iPhones, which takes a photo following a recognised hand gesture.
There's also Selfie Cam, which automatically takes a selfie when you smile.
Some Android phones support gesture-based selfies out of the box. For example, the LG G3 supports Gesture Palm Selfie.
For those Android phones that don't support such features, Whistle Camera is an Android alternative that will automatically take a selfie when you whistle and then smile.
Whistle Camera Android selfies gestures
Can I take selfies using voice commands?
Both Android phones and iPhones support the command "Take a selfie" when you call up Google Now or Siri. Unfortunately, doing so merely launches the Camera app, and the need to press the button yourself defeats the purpose of using a selfie stick.