Tone wood

Flamed Koa would make the prettiest speaker's bar none.

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 don’t 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, what’s the point.

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The one thing important about veneers on speakers is to do the inside of the cabinet too. The reason is that alot of particle boards will warp overtime when exposed to air moisture and other elements and the veneer seals the particle board (MDF, HDF, whatever type) from the surrounding environment. Obviously, as speaker enclosure with warped walls will sound different over time for many reasons. I'm sure that there are less costly methods than veneering to treat processed boards, but the point is that it has to be on the inside and outside and so this will allow the speaker to maintain its performance as originally designed. So the veneer does help the performance in that way.
The other thing it does, depending on what the cabinets are made out of, is that it may minimize the cabinet vibrating by making it slightly stronger and thicker. However, some cabinets will benefit none from it. The other nice thing about the veneer and even multiple wood layerings as another post pointed out is that the resonant properties of a 1" thick board of X dimensions are not the same as those of a 3/4" board and a 1/4" board sandwiched/glued together--the two different pieces alone change things, in addition to the glue. So the veneer will act in a comparable manner of changing the resonant properties of the enclosure walls, although on a much smaller level. I.e. don't count on the veneer alone to significantly increase the cabinet's strength, the bread-and-butter of it is in the "core" materials of the walls and bracing (if any). However, the veneer does not give the speaker any distinctive sound--speakers are not musical instruments. Any cabinet resonances are colorations and only to be supressed (with a few exceptions), the material used is only a means to an end.
A loudspeaker cabinet can only vibrate one of two ways-in phase with the original sound or out of phase, the former will augment the total ouput and the latter will null some of the drivers energy. And then technically speaking some amount energy is lost in the "friction" as the wood bends in the form of heat. The latter approach is taken sometimes, and it can eliminate the what would have been colorations; however, energy is still lost and so in the case of low-frequency drivers it can give a mush sound. I'm a little fuzzy on the latter, someone may no more. There is more to it than that. The vibrations in the cabinet can cause interdriver resonances and it can cause slight rocking of the cabinet. There's also the way the sound waves propagate from the driver itself through the front baffle hitting the edges and then the transmission to the side panels, i.e. energy is getting to the side panels from the other panels in addition to through the air pressure creating its own forces. The bottom line--the veneer will do very little for the sound of a well designed cabinet. It can help a little, but not much and not in any way the morado is more desireable than tiger maple.