Autonomously-powered (battery-less) wireless pushbutton
For anyone who is interested in a fairly straightfoward piezoelectric approach, I discovered one successful report (using a piezoelectric pushbutton from a lighter) in the following paper from 2001 by two researchers at the MIT Media Lab (incidentally the paper is titled very similar to my Question!):


A Compact, Wireless, Self-Powered Pushbutton Controller by J Paradiso, M Feldmeier - Ubicomp 2001: Ubiquitous Computing, 2001 - Springer


The following  extract from the paper summarizes their method well:


  A 4.4 μF tank capacitor integrates the charge transferred from a
  button strike. This, in-turn, powers a MAX666 low-dropout linear
  regulator, which provides a stable (although very inefficient) +3
  volts supply until the tank capacitor's charge is drained. When the
  MAX666 is activated, the HT12E digital ID encoder is enabled,
  producing a repeating 12-bit serial ID broadcast via the On- Off-Keyed
  (OOK) transmitter module.


A drawing of their circuit:


Images of their board/components:


Here are further specific details I picked up from their implementation:


For the piezoelectric/button section, they took the core of a Scripto “Aim 'N
Flame” lighter and modified the spring action to make the strike
softer.
The piezo element generates peaks around a few thousand volts -- this
is passed through a transformer, with a 90:1 turns ratio, outputting
30V at the tank capacitor.
The conversion efficiency (mechanical to electrical) for the piezo
and transformer together is 7%.
At the point after the linear regulator, they measured 0.5 mJ to have
been delivered (at 3V).
For the wireless transmission, they used a Holtek HT-12E
encoder which generates 8 bits of ID and 4 bits of data, which are in
turn transmitted by an RFM HX1003 (418MHz, 7.5 mW consumption, 50 ft
range).