Ironically, most modern Android phones now have tap-to-wake (either on by default or as an option)… Except the Sony phones.
At least on Sailfish on the Xperia 10 series you can run the following commands in the terminal:
mcetool --set-low-power-mode=enabled
mcetool --set-ps-on-demand=disabled
which will show you the clock and the weather on a dim black background when you take the device out of your pocket or when you wave your hand over the proximity sensor. This technically wakes up the screen, allowing you to then double-tap to view the lock screen. It’s not the same as the real tap-to-wake, but I find it’s close enough, because most of the times when you want to use it, the device is indeed in your pocket.
I’m still waiting for my C2, so I can’t check, but I suppose the same commands should also still work.