Glowing pressure plate
The usual method of doing this would be to use a Piezo buzzer as an impact sensor.  Something like this:  

When struck, these buzzers will produce a voltage spike.  This is exactly what they do in most electronic drum kits.  What you'd do is have a heavy backer board (3/4" plywood would be overkill, but suitable), and your lexan/plexiglass/whatever target.  Between the two are these piezo buzzers.  Depending on the size of the target you might be OK with one, or you might need more than one buzzer per target.  You'll have to experiment with different mounting techniques, but I'd start with simple double-sided tape (not foam tape).  

The output of the buzzer will be a spike that goes positive and negative, and could be a fairly high voltage (if a hand hits it).  You will want to feed that signal into an ADC, while protecting the ADC from the voltage spikes.  

You'll also have to experiment to see if this signal needs to be amplified before going to the ADC. I doubt it, but keep it in mind.  This will vary depending on the buzzer you choose and the construction of the target.

While this sounds like a lot of work, it does offer you some advantages.  The biggest is that if you have a target with 3 or more buzzers you can do a form of triangulation and figure out where on the target it was hit.  That way the target can react differently depending on if you got a bullseye or not.

I also suggest that for experimentation you get a piezo and connect it up to an o-scope.  Just hit the thing and you can see how it reacts.