Airplane Mode is easier and faster :) As WiFi is on a separate module it looks like you can do it, but you'll also lose BlueTooth. There's no telling if iOS will boot OK afterwards if that chip is not detected at boot time. Quote from: Apple A6 Teardown [コード]
If you have recently used headphones with it, try inserting and removing the headphone jack a couple of times - sometimes - especially with headphones using crappy/cheap jack connectors - the contacts inside the iPhone that detect if a jack is inserted or not will remain stuck. If this doesn't fix it: can you confirm if you can hear sounds with headphones connected ?
Without the power button, the only way to turn-it of is to wait for the battery to be depleted then you can connect-it to a power source and press the Home button to turn-it back on. Better fix that broken power button. Here's the iFixit Guide.