Chris,
I spoke to Ron Newbound, the designer of the AKSonic.
He said Corian would be fine, and sensational to look at!
But he suggested that rather than using wood screws, the (blind) holes should be carefully drilled and tapped, and metal screws inserted to hold it all together.
I think Nicholas' idea of using polyester adhesives is a good one too; in which case undersized holes with metal self tappers as used in autos perhaps to hold it together during glue curing. You could leave them in, of course.
Great care would need to be take not to overstress the material, as it may crack, and you should roughen the mating surfaces before gluing and take advice on the best adhesive. And keep a close eye on the length of the screws, lest they break through the front face of the speaker and ruin the appearance!
I understand Corian is vulnerable in hot environments. This makes it unsuited to Class A power amplifiers, but I would have thought ideal for speakers. And it is lovely to work; softer than aluminium, tougher than most woods.
It looks sensational, like something mystical out of Lord of the Rings!
Another alternative is a standard timber construction, surfaced with a 'stone', acrylic finish. This is how Nicholas has done his speakers, clearly visible in his avatar. They look like some kind of space age rock, I call them his tachyon generator, and whenever I visit I suggest he take them to 'Warp 7 Scottie!'
Cheers,
Hugh