what sensors to use in touch sensitive furniture
You can use a capacitive touch sensor for this sort of thing -- no pressing of any buttons is required.  

You need to create 3 things for this to work:


A sensor PCB which has two metal pads. Mount this inside each of your wooden pieces near the surface.  When the user's finger gets close enough, it changes the capacitance between the pads.  See this application note for some tips on how to design the sensor.
A sensor IC wired to these two metal pads which senses the changes in capacitance.  Something like the AD7147 could work as the measurement chip.  
A controller of some sort to communicate with the sensor IC and light up the appropriate LEDs.