answer this definitively but... The waveshield has a 3.3 volt regulator for the SD card. That would not be needed (and not work) at 3.3v. Voltage regulators need a certain percentage above the voltage being regulated to work. The Wave shield also has a level shifter for the SD card which would also not be needed.
I "think" if you built this wave shield you would have to solder in some connections where the voltage regulator would go.AGAIN
... you should confirm this with Adafruit.
The operating voltages for the ICs listed on the board (parts list is here: http://www.ladyada.net/make/waveshield/parts.html
) all seem to work with voltages as low as 2.7 volts according to their datasheets. You should confirm this yourself however.
The WaveHD library did compile with Arduino 1.5.1r2 beta but whether it really works well... I cannot say since I don't have the shield.
I have not seen any list of Due compatible shields except to say that all the 'official Arduino' shields will work. if you come across such a list I am sure people would appreciate it being posted up.
If you have any shields you are interested in using on the Due your best bet is to email the vendor and/or post the question on the official Arduino Due forum. Also you can download their library(if they have one) and try compiling it first.