How can I conveniently pause and play my iPhone audio with minimal touching of the phone?
The WATCH has been released since this question was posted. If you’re open to buying one, you can of course play and pause by speaking to it. “Hey Siri, Play/Pause.”

Even without an WATCH, starting with iOS 8 your iPhone can also respond to “Hey Siri.” The feature is enabled by going into Settings → Siri. Enable both Siri and Allow “Hey Siri”.

On the iPhone 6s and above (including iPhone SE), the low-power M9 motion coprocessor allows this feature to be invoked at any time (provided the phone is not face down on the table, or in your pocket).

Earlier models can activate the feature while plugged in to a power source.

“Hey Siri” will allow you to start playing music without touching your iPhone.

Stopping it is trickier, and requires the volume to be turned down very, very low. You have other options, of course, such as Control Center, Lock Screen Music Controls, Today Widgets (depending on the app) and manually invoking Siri by long-pressing the Home button.

It’s also worth mentioning that the built-in Music app prevents the screen from locking if music is playing while the iPhone is plugged in to a power source. The display will dim after a while, but a simple tap will light it back up without asking you to unlock it. Other apps may do the same.