A veneer should have little or no affect on the tone of a stoutly built speaker enclosure, especially those such as the Avalons stated above. Speakers made out of solid wood such as Diapasons I suspect would have tonal shifts depending on the type of wood used. However, they use very dense hardwoods, which may exhibit more inert characteristics than MDF designs. Roy from GreenMountain Audio uses sheets of sorbothane sandwiched between the MDF and quarter inch planks of hardwoods to eliminate any coloration the purely decorative hardwood coverings may induce. I have Gallo speakers made out of aluminum spheres. They are devoid of any woody or boxy sound, however I have always felt they had a bit of a metallic sound. I dont know if it is due to the material itself, the lack of any wood in the design, or the sonic character of the CDT tweeter.
My advice on selecting a veneer is to match the color of the wall you will be facing while listening. Choose light colors with light colored grilles for white walls and dark speakers for dark walls/wood backgrounds. This will create more of a psychological disappearing act for the speakers than any tonal difference one could detect between veneers. My speakers are all black, and I painted my listening wall a dark plum. If there is a speaker finish you must have then the other option is to listen with the lights off or eyes shut, but then, whats the point.