Wood is fine, provided all external metalwork is grounded. Preferably, major items of internal metalwork too, such as mains transformer frames. Check that if the live mains lead became free the unit would still be safe, whatever the mains touched.
You will have to take more care over screening/shielding with no metal case to keep out interference. A large piece of grounded metal inside will help.
One trade-off was that I had to lean on a friend with metal cutting tools.